Using 'generify' to mean 'to make generic'?

Solution 1:

Genericise / genericize is the version I most frequently hear. Out of interest, I ran an ngram test, with generify not getting a single hit. Genericize, however, has risen in usage from the '80s.

Solution 2:

Generify is certainly the right word to use in the context of Java generics.

This is from the Java Language Specification preface:

Joe Darcy and Ken Russell implemented much of the specific support for reflection of generics. Neal Gafter, Josh Bloch and Mark Reinhold did a huge amount of work generifying the JDK libraries.

In other fields, genericise / genericize would be better recognised, as answered by Mr. Disappointment.

Solution 3:

The dictionary doesn't display a result, but does come up with "generification", which I assume is where "generify" comes from.
There's the alternatives of "generalize" or "abstract".