How do I properly configure an EntityManager in a jersey / hk2 application?

One option is to instead of creating a new EntityManagerFactory in the EMFactory (which is in a request scope), you could create a singleton factory for the EntityManagerFactory, then just inject the EntityManagerFactory into the EMFactory.

public class EMFFactory implements Factory<EntityManagerFactory> {
    private final EntityManagerFactory emf;
    public EMFFactory (){
        emf = Persistence.createEntityManagerFactory(persistenceUnit);
    }
    public EntityManagerFactory provide() {
        return emf;
    }
    ...
}

public class EMFactory implements Factory<EntityManager> {
    private final EntityManager em;

    @Inject
    public EMFactory (EntityManagerFactory emf){
        em = emf.createEntityManager();
    }
    public EntityManager provide() {
        return em;
    }
    ...
}

Haven't tested this exact implementation out, but it should look something like this. I've used this pattern before.

register(new AbstractBinder() {
    @Override
    public void configure() {
      bindFactory(EMFFactory.class).to(EntityManagerFactory.class).in(Singleton.class);
      bindFactory(EMFactory.class).to(EntityManager.class).in(RequestScoped.class);
    }
});

UPDATE

One thing to note about the above example is that it doesn't clean up resources, i.e. the EntityManager should be close; it won't close itself. There is a dispose method in the Factory class that we need to override, but from my experience, this is never called by Jersey.

What we can do is add the EntityManager to a [CloseableService][1]

public class EMFactory implements Factory<EntityManager> {
    private final EntityManagerFactory emf;
    private final CloseableService closeService;

    @Inject
    public EMFactory (EntityManagerFactory emf, CloseableService closeService){
        this.emf = emf;
        this.closeService = closeService;
    }
    public EntityManager provide() {
        final EntityManager em = emf.createEntityManager();
        this.closeService.add(new Closeable(){
            @Override
            public void close() {
                em.close();
            }
        });
        return em;
    }
    ...
}

This way the EntityManager is ensured to be closed at the end of the request.