Both the red and white oak groups of species have enough tannins for a couple of very old-time, very old-school finishes. You might consider these.
a) ebonizing = a brew of iron (steel wool) and vinegar (acetic acid). the iron acetate reacts with the tannins.
b) fuming with ammonia. I've seen the works of other wood carvers done this way. Real ammonia in a dish, outdoors together with the carving(s) in a garbage bag. Other woods like birch require a preconditioner of tannin (aka 10x strong tea.)