Avery offers free templates for business cards that can be used as loyalty cards or punch cards.
Just choose your business card to print yourself at https://www.avery.com/products/cards/type/business-cards
Or choose a business card for Avery WePrint to print for you at https://www.avery.com/custom-printing/cards/business-cards/
Then design it using Design & Print Online at avery.com/templates and on step 2, choose template, search on Loyalty and you will see all the designs available.
For more ideas, check out our article: https://www.avery.com/articles/build-a-loyalty-program-with-punch-cards