Right now one of the fastest was to get CXP is to farm the snowball holiday quest, which can be repeated endlessly and gives 20 CXP per turn-in. BioWare has confirmed this is intended and is not considered an exploit.
Yep, a holiday mission is the true endgame right now -____________________________-
Laughed harder than I probably should have, but he's pretty spot on. That's been BW's usual response to everything, completely missing the point of why everyone doesn't like something and making a change that misses the mark bigtime.