The best solution is to not mandate them IMO. If you create strong incentives for fraud with something that’s difficult to authenticate then you shouldn’t be surprised when it happens a lot.
The standard EU Covid passport is a QR code that contains all the data cryptographically signed, which is much more difficult to fake that a card filled by hand...
(What's preventing one person from copying their cryptographically signed card?)
The card includes the holder's name and DOB, I believe, so along with showing ID this makes copying a card useless.
The only alternative I can think of (assuming we do want secure Covid 'passport') is to have a picture taken when you get your jab and include that picture in a secure card... That's probably more difficult to implement when the vast majority of people have a photographic ID (ID card or driving licence, or even passport which is a very common document to have in Europe).