I set about digging around trying to find some clubs that might have some tradable commodities. The first club I came across was the Royals, who have bullpen needs as well, but may be willing to part with a couple pitchers in exchange for some larger parts in their continuing effort to rebuild their club. Within this article, it is mentioned that there are rumors circulating that Jeremy Affeldt and Jimmy Gobble might be on the trading block. Both are left-handed, and both are affordable making $1 million and $345,500 respectively.
Affeldt has been used (unsuccessfully) as a closer in the past, and still has a lot of raw talent. Gobble has been back and forth between the majors and the minors the last three years, and until last year was primarily a starter (and not a very good one at that). Affeldt would probably attract the most attention as a left-handed power arm out of the pen.
For the last several days there have also been rumors swirling around the Braves camp about Cubs reliever Scott Williamson. He is a right-hander who has closing experience, but the Cubs may be asking for too much in return. But if Wood and Prior can't pitch, and the guys that might replace them are not doing well, then they may be forced to make a move to get another starter, and that is where the Braves trading strength will likely come from.
I'll do more digging as the week goes on, and see if I can find some more juicy rumors.