Anything paper is useless and it will be knocked off in no time. There has to be something that can be verified by the vaccinating country and tied to the person asking for verification, which means it must be tied to a verifiable ID (passport, national ID) in one way or the other.
IATA would have been ideal as they already have the network, the app and all it would need is a country's immigration and the vaccinating government to tie the relevant parts of the vaccination database to it and allow it to be queried - all securely.
If every airline and/or country goes it's own way, and immigration officers are expected to evaluate a mass of disparate forms of vaccination verification, there are going to be some long waits at airports in our future IMHO.