All vintage base ball equipment of the 1860-1870's era of base ball was hand made and/or home made. Bats were made out of axe handles or wagon wheel spokes. Balls were hand stitched lemon peel balls, and all storage for the gear was made of wood or canvas. The website - 19cBaseBall is a great resource for viewing vintage drawing and catalog pages of base ball equipment.
According to Beadle's Dime Base Ball Player, published in 1860, bats were to be between thirty and forty inches and weighing about 48 ounces. Bats were usually made of ash, but could be made of maple, hickory and pine.
Bats didn't become limited until 1882, when 42" was the maximum length a legal bat could be.
Today, vintage bats are made by a few companies, including The Phoenix Bat Co. which made the first Cleveland Blues bat, the "Tomahawk". Many teams make thier own bats, if they have the luxury of a ballist who owns a lathe and woodworking skills.