Here are a few guys I think would help the C's that are actually a possibility to get. Even with a new CBA coming in it's obvious who's going to be in our price range.
Free Agents:
Shane Battier: He could back up Paul Pierce and/or Jeff Green and is a good locker room presence. Memphis will look to resign him but Marc Gasol will be a bigger priority for them.
Jamario Moon: Same as Battier. A veteran who could back up the 3 spot. Not as good as Battier defensively, but would be a nice addition.
Kris Humphries: Would definitely fix the depth at PF. NJ is going to push hard to resign him, but if they don't, the Celtics should try to get him.
Greg Oden: Greg Oden could have been one of the most desirable free agents this off season, had he stayed healthy and dominant. He's an RFA this off season and I don't think Portland has the money or patience to resign him. He won't cost much, but the Celtics could attract him.
Alexis Ajinca: he's not a "good" center, but he's 7'2" and could take all those regular season minutes away from Jermaine and let him prepare for the post season.
JR Smith/Arron Afflalo/Wilson Chandler: Either one of these 3 Nugget shooters would definitely help the Celtics scoring droughts.
Deshawn Stevenson: Attitude problems, but a good defender. Although likely to resign with Dallas after winning the championship, but they might let him slip away focusing on Butler and Chandler.
Kwame Brown: Could eat up regular season minutes at center, and actually had a decent year last season.
Joel Przybilla: Another center the Celtics should look at. Might cost more then Kwame/Alexis though.
Eddie House: Not sure he would come back to Boston or reject his player option with MIA after getting to the Finals. But his 3 point shooting would help a lot.