Now you are really leaving my area of expertise. In my opinion, far from expert opinion,
the biggest thing that kills off dragonets is not getting enough food. So I'd say build your tank to be mandarin friendly. This could take multiple approaches.
Approaches. Listed in my personal favorite order)
1. get your dragonet eating non-live food and make sure you have way to feed where they have a chance of getting it. This could be a large mixed tank that is over-fed by most standards and the pumps off for at least 30 minutes so they have a chance to get some (also squirting food in more than one place, one by them and two in other places to attract the tangs LOL) (my 125 mixed reef tank). This could also be a smaller specialty tank that they are they only thing in the tank (my 30 gallon ruby red) Note this can be combined with approach 4 (my personal approachis a combination of 1, 3 and 4 when I get the time I'll probably add number 2 in).
2. You get them used to a feeder and make sure you have a spot in your tank for a feeder (this can be non-live food or live food). Build your rock where you can hide your feeder if you care. there is a pellet diner and a live brine feeder that both work great. google mandarin diner and paul B's feeder.
3. Spend money and or time. This approach can work well if you have the money. For about $50 you can get many, many amphipods shipped to you. Your fish will love you. Depending on your rock work and other parameters, you'd need this every 2-4 weeks. (Not my favorite approach but I like it better than approach 4). You can also cultivate copepods if you are will to run live cultures in containers outside your tank, takes time and an initial investment.
4. Depends solely on you tank to produce the food. This is the approach often espoused by the elite commenters. This means you have a very large tank with lots of rock work that you let age for 6 months to a year and if you are lucky you can keep one mandarin. The upside is you don't have to bother to train your mandarin onto other foods and they won't starve. The downside you need 90+ gallons and lots of wait time for 1 Mandarin. so you'd need more than that for multiple dragonets.
This is my own opinion so please don't take it as fact but weigh my arguments for your self.
I believe that shortly after you cycle your tank you could support multiple mandarins if you follow these simple beliefs....
1. Fish are healthier if they eat. You are responsible for them eating.
2. Mandarins eat copepods, amphipods, not harmful isopods, ostricods, (mine have even eaten white flatworms) naturally.
3. They can be trained to eat live brine, frozen brine, pellets and I've heard frozen mysid but never seen it in my 7.
So for several of my tanks I have...
1. purchased tisbe pods and start a culture. Their life cycle is relatively short though lots longer than rotifers. They get to sexual maturity at 6 days and have a generational cycle of 11-18 days. So babies start having babies..... Tisbe's are detritus eaters and so you don't have to have live algae you can use flake food, yeast what have you. I put them in pop bottles and plastic shoe boxes. Do this step early.
2. Cycle your tank. Make sure it is cycled. This is 10 days to 6 weeks. Make sure you have nice rock work. I'd recommend some macro algae like chaeto or caulerpa (though not necessary). Some rubble piles at the base of your rocks.
3. Seed your tank with 50% or more of your copepods you been growing. Spring for some amphipods and seed the tank with all but 50. You can culture amphipods but I've found them harder to culture separately than copepods. They do grow well in the tank.
4. buy your dragonets. Keep them in small quarantine containers (or large but by themselves) if they are skinny (most of the ones you find in LFS are) feed them live amphipods, brine shrimp, copepods but also let them run out of those things in other words only feed 6-10 amphipods in the tank at a time. 2-5 times a day try some frozen food of some kind, brine, mysid, rotifer, copepods. Mine have always ended up on frozen brine (enriched before frozen). make sure you squirt it near them where they can see it fall. You can also try garlic soaked sinking pellets. Mine always start with watching the brine fall and eventually eat the brine. I don't think any of my dragonets have taken longer than 10 days ( less than recommended quarantine time) to start eating brine. But I make sure to give them live food in the meantime. One advantage for live brine is you can gut load medicine as part of your quarantine. Mandarins don't get ich much but can get flukes and intestinal parasites.
5. Once they are eating brine and you are sure they are safe put them in your seeded tank but still feed them their non-living food daily (2x daily to me is the minimum). You've kept back some copepods so you can reseed every once in a while their favorite healthy food. The copepods and amphipods will reproduce in a healthy aquarium and will act as part of your clean up crew. But if you didn't get a large tank or if you have to dose for disease or if you get certain algaes or dino your population may decline. So when it is over reseed. Also think about the other fish you get make sure you don't load up on too many copepod eaters. tangs, banggai, clownfish these don't ravage a copepod population. small wrasse, some gobies, pipefish, seahorses these all eat copepods as vigorously as dragonets. Many of these other fish can be trained to a feeder as well.
6. be prepared to reseed. I reseed amphipods about 3 times per year. I just ordered 2000 because I'm going on vacation so I'll dump those in my multiple tanks and won't feed at all while I'm gone. The fish will hunt naturally and have lots of copepods and amphipods to eat. My dragonets and tangs will be in the best shape (tangs because I have 5 different macro algaes in the tank). My banggai and clowns might be hungry when I come back but because they are fat and happy before I leave they'll be fine. All my worst tank problems have occurred when I left for vacation and someone else came to feed. This will be my first nobody coming vacation so we'll see how it turns out but I know my dragonets will fair the best as they are getting copepods and amphipods dumped in the tank right before I go. It also is cheaper, I spent $44 on the amphipods (including shipping) which is less than visits from a pet sitter.
Now you could probably never feed copepods and amphipods if they are eating frozen or pellets. But I think they will stay healthier if they get some natural foods and this also allows them to pick all day since they have short digestive tracks. The non-live foods like brine give them large top offs to their stomach meaning they don't need as much live foods and also means they'll eat less copepods which allows them to reproduce and keep the population up. I've had my Mandarins almost a year which isn't long but I take the fact that she is getting gravid and he has put on some weight as signs they are doing well. My ruby reds I've had less than that but continual spawning speaks to their health (remember they had concave stomachs when I got them). I can also tell you my ruby reds I was so worried about them I didn't put them in the 1 gallon quarantine I put them in my frag tanks that also had large amounts of copepods. but I still fed them brine and pellets 2xdaily. They eventually started eating the brine even with clouds of copepods so they too appreciate a large meal without work LOL. The male will now swim up and eat out of the water column. All three of my new spotted mandarins are now eating frozen brine (exclusively since they are still in quarantine).
Well you asked for it. I hope that rant helps you. Feel free to ask follow up questions. I don't see Mandarins as a fish you can't keep without success I just view them as needing some very specific steps. I'd rate them as difficult only due to you can't just buy one and throw it in a tank with anything. But I also don't agree with those that say only a large fully developed live rock tank can handle them after a year of waiting. Food is food you can jump start those copepods and due to their short reproductive cycle you can up your population quickly but more importantly with training your fish won't rely only on copepods.
I needed to add that I think the tank should be relatively low flow compared to the standard reef tank. My mandarins are never so active as when I turn the pumps off. I should also add this is the setup for mandarins and dragonets. It can cause problems for other things. Like when you over feed you can get a break out of nuisance algae, corals may not appreciate low flow. But I set my tanks up with mandarins in mind and then add other things as I think I can. I don't have a sps tank that I try to add a mandarin to. Btw I do have sps, my montiporia (easy to grow) had sent from 1" square to a beautiful 6-8" oval. But if it comes down to the monti or the mandarin the monti loses. The top of my tank has more flow than the bottom allowing me to sneak in a few sps near the top of the tank and I still have to use a turkey baster to blow off the monti once or twice daily when done feeding.