2 days plus and no one else stepped up?
So not coming from a deep technical wood background?
There are ways to manage almost any wood for cue building, if you have the background.
If not, then you are sort of trying to attain ("master") 2 areas of expertise at once.
First - just telling you that (as an example) rosewood, or ebony, or even mahogany are "stable" would be true.
One of the reasons (as well as mass and good looks for the first 2) they were all used for cues. However, if you are not a woodworker, you would not know how to eyeball a piece of wood and judge whether it was a good candidate for staying stable. That depends on grain, how it was cut in the tree, and how (or whether) it is dry. Some cuts, usually the most spectacular visually, are really not stable. I'm of the impression (from specifying lumber for millwork, being around/using lumber, and seeing some cue blanks) that some wood sold as cue wood is mostly the scrap from other operations. That is not necessarily a bad thing. I made my first cue from a beeswing figure off-cut from manufacturing a run of custom flooring in my shop. When getting into really expensive exotics, some might be cut from branches or trees that grew with a substantial lean, and will be much less stable than trunk wood from a straight bole.
Cue makers get around it by coring, and taking years in process with drying. Some more than others, we all have theories that (mostly

) work for ourselves.
If you buy wood as lumber, it is generally supposed to be "dry" to some *uniform* condition throughout the lot; unless specified otherwise.
If you buy it as "turning blanks" it usually is understood in the lumber trade that dryness is not a requirement, and any 2 pieces might or might not be of the same dryness.
Some cuemakers core every butt, regardless the quality of the appearance wood. No reason not to. Types of wood like burls can be used without much risk if any, if they are stabilized (professionally, or learn to do it in shop if it interests you) & cored. ETC, etc.
What construction method do you envision for your custom cue making?
PH is generally pretty stable. Mahogany is a by-word for stable, though not much in favor these days because it is soft and light. Honduran rosewood is not terribly expensive and looks good. IME avoid "Bolivian" RW. (Pau Ferro, actually). it is a fun wood for some things, but not very stable, and unlike Honduran, it is not a real RW. I love bloodwood for lots of things, but it is another that is not intrinsically stable unless the cut and material as received are near perfect. The caveat for any of them is "so long as the grain is good and you know how to manage the drying".
Basically you have to go for it, make a few, take chances and experiment.
There's a guy on the owner-build cue forum that must make almost a cue a week, out of anything, and they look great!
Good design eye, too.
Peruse that section to get some ideas.
good luck!