A printer service probably don't want to print such cards. I am not a lawyer, but the way it has been explained to me is that from a legal perspective, they print the cards and sell them to you. If you have them print cards of your design you basically license them to print that design on a set of cards.
The printer could be in legal trouble if they print stuff and sell the printed materials to you.
Quote from The Game Crafter:
Can I make a game using copyrighted items if I don't intend to sell it to others?
We are not able to print games containing copyrighted items used without permission, even if they are intended for personal use only.
It doesn't mean all print-on-demand services verify or comply to this, but this is the legal stuff what I understood from TGC staff.
Some services out there try to move the legal burden to you by having you tick a box "yes I own all rights", but in the end AFAIK the printer could still be sued for infringement if they knowingly print and sell you the stuff.