I haven't seen any JPA providers with built-in support for hstore.

Unfortunately there's also no type extension SPI for JPA, so the is no
standard way to provide extension types that don't depend directly on a
particular JPA provider's guts. Frankly I think the concept of JPA for
fully provider-independent portable dev is a waste of time for anything
except toy apps or very small databases - anything real generally needs
per-query fetch control and other things JPA just doesn't provide for.

I suggest picking a provider and sticking to it.

If you're developing a new app, rather than targeting hstore, consider
starting work with PostgreSQL 9.4 (currently in beta-2) and using the
jsonb type. That way you can use the numerous good quality json tools in
Java to map json to/from Java objects or manipulate json trees, while
saving them to the DB and loading them from the DB as native json fields.

If you use hstore, you'll have to write the equivalent yourself or crib
from someone else. So why not start on the right foot and go straight
for jsonb?