It's surprisingly hard to find a suitable carrier -
Ryanair - Nope, they seem quite happy at BOH plus the runway/stands are useless for them.
Easyjet - Unlikely, fairly close to LGW, runway less of an issue but stands still can only take 2 A319/20's at a time.
Thomson - Tend to fly a mix of shorter and longer routes so the runway is too short as are the stands, plus they also seem happy at BOH. However some extra W pattern flights to PMI could appear next year if they have room to in the schedule.
Thomas Cook - As above, could see the odd W pattern to the Balearic's at best.
Monarch - Still quite unlikely due to stands (notice a trend?) but they do fly more <3 hour routes than TOM/TCX so the runway could be less of an issue. I'd say they have a small outside chance.
Jet2 - On paper they seem the most suitable, stands are less of an issue for the 733's however I question whether they would want to start flying from t'south where they have far less brand recognition.
As for foreign carriers Vueling could take a second look and have an operation similar to their CWL one. HOP! could look at serving Nice if the demand is strong enough for a foreign carrier with less recognition in the UK to serve it. Volotea would be an outside suggestion...