I don't know about the closer role with Piniero. He posted an ERA over 6 last year playing in a very good pitcher's park. Now he's out of the offense-less AL West and is jumping into the AL East in one of the best hitter's parks in all of baseball. I have no confidence in Piniero emerging as a suitable closer.
As of right now, the Sox have nothing but a few servicable middle relievers in the bullpen. They need a significant signing and/or trade to truely upgrade. It looks like it's too late to make any big signing now bc there's no one left on the market.
Right now I'd say the Sox best option is to keep Papelbon at the closer spot and sign another starter or use a mix of Piniero, Tavarez, and AAA guys until Lester is healthy. They should be more careful about overworking JP by giving Timlin or Donnelly save opportunities when Papelbon needs rest. If by midseason Papelbon is really unhappy, they'll hopefully be able to trade for a closer on the block and then Papelbon could slide back into the rotation.