Are there any alternative to SQLite to use as embedded database engine?
Sure. This page shows a couple non-SQLite frameworks (besides Core Data):
I have no idea how awesome these projects are, so YMMV.
If you're looking to avoid external dependencies (ie, not shipping a framework with your app), then you're stuck with SQLite or CoreData. CoreData can use XML as its format, but it has some disadvantages. SQLite is definitely the most recommended CoreData backend.
There are a couple of alternatives to SQLite
if you want to have an embedded database engine, such as:
Be sure to also check the licensing terms.
EDIT:
Firebird is licenced under a derivative MPL
licence, so it can be used in closed-source
applications (see FAQ). The other two are dual-licenced
so you need to pay if you are going to use them in commercial applications.