Something with board games and AI. Perfect play with a trivial game seems too modest a project
I disagree. For a 9th grade that's not so very easy. For example Tic-tac-toe has 0.3M possible game plays, so one could implement searching in the tree, and then using symmetry to reduce the the tress size. You have to know how to backtrack, build and traverse a tree. That might seem trivial to us, but isn't for somebody who has never done it before.
Another game that might be interesting and not too hard if done imperfectly is Connect Four, but I wouldn't inflect that on a 9th grade.
Encryption. Probably something involving frequency analysis to break substitution ciphers.
I think that's quite a nice one, because you can get a result rather quickly, but still can optimize quite much (for example you can use a dictionary, digraph and trigraph tables that you build from the dictionary etc, but you already get some intermediate results for longer encrypted texts by using very simple approaches).