After years of having bigger tanks that grew all colors of coraline like crazy I was forced to downsize to smaller tanks after moving for practicality sake. First problem I ran into was not being able to coraline. I've always considered tanks that grow healthy coraline to be stable and healthy and found tanks that didn't to have other issues. Then again I know plenty of reefers who have healthy SPS tanks without coraline, so it's just my personal experience. There are healthy tanks that don't grow coraline, but I've never had a tank that grew healthy coraline that wasn't also a good over all tank in general.
I spent a summer setting up different small tanks and setting up various water params to try and resolve the issue along with taking notes on friends tanks that grew strong coraline. I didn't come up with a smoking gun, but I did find some variables with water quality that added up and I'm 90% certain they have something to do with it.
First, Coraline seems to require high solution amounts of calcium carbonate availability in the water column. Calcium takes many forms in a reef tank, but calcium carbonate is the one that keys coraline growth the most. Most of the calcium we add is in the form of calcium chloride (basically sidewalk de-icer) and this does not seem to help coraline growth. Note how tanks that run calcium reactors, use crappy well or tap water, have deep and established crushed coral beds etc all seem to have less problems with coraline growth. I found I could get a coraline to explode in a small tank by throwing a couple cups of dry crushed coral in it to the point the water was milky. I could run calcium levels in that same tank via test kits below 300, and yet coraline exploded.
High mag levels seem to help, likely keeping calcium carbonate molecules more soluble just like ionic calcium (theory)
Coraline also seems sensitive to low pH. Using kalk topoffs combined with not obsessing with calcium chloride levels caused coraline to take off.
Strong directional lighting like high powered LED fixtures seems to discourage coraline growth.
Coraline likes strong water flow. High water flows over crushed coral beds is a bonus along with some nitrate.