Well, if you can save the game using the in-game save, at least it lets you play the game, right?
The odd ROM here and there won't let you save states unless you adjust the settings. What settings to use for this game? I wouldn't know for certain. Perhaps someone else can help you with that.
Chances are, if you're tried every save option you can, then you won't be able to use save states/snapshots unless you:
1. Try a different ROM (of the same game)
2. Use a different emulator
3. Wait for an update for your current emulator
Otherwise, you might just have to play semi-legit and use those in-game saves : P