Well, provided that this doesn't need to be highly secured. You could base invite keys on some property of the verification code. For example, you could design a system where a code is valid if the sum of the first five digits is equal to the product of the next three digits.

A system like that is easy to code and requires no database. The downside is that your would be relying on security by obscurity. For something like an invite system that may perfectly acceptable.