Paperless Post offers free card designs that can be sent to up to 2,000 recipients. When you’re browsing card designs, you can filter your results to show only free cards, or you can check the pricing information in the template preview to see if the design you’re looking at is free to use.
Any card designs that are advertised as free will not have a coin cost, but you may need to remove Premium options (like envelopes) from your Customize page once you get started.
Here are the direct links to free invitations and free cards.