What you can do is veneer a piece of paper or chipboard to the back of a baseball card. Then you would cut the card smaller so that it is business card sized. This will also hide the fact that it is made of two pieces of paper. You can use glue, but that will warp the paper. Use Xyron, which is available at any craft store (This is the staff that makes anything into a sticker. It is acid free.) Then letterpress print on the reverse and you have a business card on the back of a baseball card.
If you want to keep it the size of a baseball card, then you have to veneer the card and then carefully trim it to about the size of a baseball card, but SLIGHTLY smaller. This will also hide the veneering...
Bill