From my point of view, there would be a few options to pull off a sign and trade of Davis.
1. It could be to a team that is over the luxury tax, and need to sign and trade for him, in order to compete with teams who can offer him the larger MLE.
2. It could be a team under the cap, who like him, but would like to preserve cap space, and have guys who they might not need as much under contract.
3. It could be a double sign and trade, where a team who wants Davis, sign and trade someone they don't want to resign to the C's.
4. (and I love this one, if they can pull it off), a team under the cap takes some cash from the C's to sign and trade for Davis, creating a trade exception for the C's.
5. I believe the C's would be able to use the Amnesty provision on someone they trade for who is already under contract, so they could get someone with more than 1 year left on their deal, use them for the year, then cut them next summer, if they want the cap space.
With all that said, the trade that makes the most sense for both teams IMO is Davis to Indiana (who desperately need a PF), for Dahntay Jones (they don't need him), and a resigned Jeff Foster.