A few relievers were non-tendered, many of whom have once had moderate success and could be cheap options. I know little about any of them though, so I don't know if any are better than internal options. Here's a list of non-tendered relievers:
Takashi Saito, Scott Proctor, Yhency Brazoban, Clay Hensley, Charlie Haeger, Chris Britton, Matt Belisle (has been starting mostly), Gary Majewski
Also, Jonny Gomes, who kills lefties, was non-tendered, but I don't see where he'd fit if he can't platoon with Branyan at first.