Why do you pick up class or module of study if you not even trying to participate?
As I'm sure you didn't read the announcement on the top of Java section I will recommend to visit the link "We only give homework help to those who show effort"
As for the idea, nobody is stopping you in coding of simple chess game player vs player, where you will need only to check if the player made valid move and if he made or got into "check" or "checkmate". However this will "fly" only if teacher did not specifically made request for AI in the game

:'( please help....
can you give me a full program of a game using java?
i don't know it...
please give me some idea...
give me game program, the important is it is a game... please
thank you and God bless!!

to answer the only question you've asked:

why, yes, we can.

to answer the next question you're about to ask, after reading this:

why, no, we won't.

about giving you some ideas...

I've seen Risk being written in Java, there are the classics like 'snake'
you could make something like 'find-the-matching-pics' (or however that's called in English), or a simple guessing game, in which the player has only 5 tries to find a 3-digit code, ...

each game can be programmed in Java, just pick one you know and like, start coding, and let us know when you run into any problems

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