You're not going to find a hardwood stock in anything that is a multi-shot BB repeater. Warden Wolf explained the market fairly well, and all the nicer, higher powered air rifles marketed towards adults are the only ones with good hard wood stocks, but they are no good for BBs ( steel BBs wear out the rifling anyway, but mostly because the way they are loaded ) and they're only single shot.
I think the closest you're going to get what you want is something like a Crosman 2100 or a Daisy 880 or 953. They are ten-pump variable pump guns. The Crosman 2100 has a 17 shot internal magazine for BBs, and the Daisy's have an internal reservoir that deposits a BB into the chamber when the action is pulled. You have to fire pellets one at a time with the 2100, but I believe the Daisy models accept a 5-shot cilp that you can push through the action one shot at a time.
I can personally recommend the Crosman 2100 ( also branded as a Remington AirMaster77, same rifle though ) as I've had great results with it inside of 25 yards. Penny sized groups are easily accomplished. I personally feel like 30-40 yards it starts holding groups a little less tight ( maybe an inch or two ), but I've pested crows and ground squirrels with it at that range so you can still do plenty of plinking with it.
One thing you're going to want to realize right off with accuracy... BBs and accuracy do not go together. You might be able to use lead balls, but they probably will not make good contact with the rifling so won't be that accurate either. Steel BBs on the other hand will wear your rifling down, so you shouldn't mix the gun you want to use for BB plinking with the one you want to use for any sort of long-range shooting.
In any case, if the plastic stocks are really a deal breaker, you might be able to find both an older 2100 or 880 that are still in wood, but there's no telling if the rifling in them is still any good since they were intended as BB/Pellet guns.