What is a godly vessel?

the human soul

The exact pairing "godly vessel" does not occur in the King James, New King James or Standard translations of the Old or New Testaments. This is close:

2 Timothy 2:20, 21 - But in a great house there are not only vessels of gold and silver, but also of wood and clay, some for honor and some for dishonor. Therefore if anyone cleanses himself from the latter, he will be a vessel for honor, sanctified and useful for the Master, prepared for every good work.

The "vessel for honor" is not just the soul, it is a soul that has been cleansed (Acts 22:16), sanctified (Jude 1:1), made useful and readied for service (2 Timothy 2:15).