For coralline algae you need to add a small rock with coralline algae on it, it will spread from the added rock. You will also need to be sure your calcium is up to at least 400 ppm but preferably between 425 and 450, alkalinity between 8.0 and 11.0, magnesium between 1300 and 1400.
How do you control Calcium, Alkalinity, and Magnesium?
If all you have is coralline taking up calcium, it's pretty safe to say that you should have what you need by using Reef Crystals for salt, or some other salt that has a reasonable amount of minerals/elements. I wouldn't go crazy changing a bunch of parameters in a FOWLR if all you are looking for is coralline growth. It's more hardy and easily-grown than SPS. I'd pick up a calcium test kit, and keep it anywhere at or above 400ppm.
In a decently-established tank like yours, it won't take long for coralline to start growing, once introduced. As was mentioned before, I'd just get a piece of live rock or two that already has some varieties growing in them and put them in the tank. In my opinion, having a good variety of 6-8 different kinds will help cover more parts of your tank at a quicker pace. Different species like different conditions, so more is better.
To get it seeded quickly in your tank, you can take scrapings of each kind (scrape the rocks, or the shells of snails/hermits if you buy some with coralline on them), and gather the scraping into a small bowl with some tank water in it. Optionally, you can use a mortar/pestle to crush it up, but scraping it with a knife with already grind it pretty well. Once you have a bunch of scrapings in the bowl, just pour it in front of a powerhead or just all around the tank.
Trust me though, it won't be long until you are cursing this stuff because you have to constantly scrape it off the front and side glass.