Any fruit wood has the potential for being a good stock wood. I have seen persimmon wood, it is reddish wood beautifully streaked with brown, and would make a very attractive stock. That said, making a stock blank from a tree is no easy feat, involving debarking and sealing the log, drying the wood for several years, quarter-sawing the log, and carving the stock after sawing. You could just as easily buy seasoned wood from a wood wholesaler and be time and money ahead, but if you feel you have the skills and the patience, by all means give it a try. I have seen very nice gunstocks made from apple, mulberry, almond, pecan, hickory, cherry, you name it.
The main reason most gunstocks are made from walnut is that walnut has just about perfect qualities for stockmaking: it is strong and dense without being overly heavy; it is hard without being brittle or checking easily during working and yet cuts very easily; it is flexible and strong without being too limber. Walnut is pretty much the perfect wood for gunstocks, and furniture makers like it for the same reasons. Another reason is that large orchards of walnut trees are grown commercially for the nuts, and they are harvested at about 50-75 years old as nut production declines, and new trees are planted. This makes good quality walnut lumber common enough for industrial use.