Southwest does not accept Continental points. They operate very independently, and other carriers generally won't accept their tickets either.
The only domestic carrier that I am aware of that you can use CO points on other than CO is NW, because they code share a lot of flights. I'm not sure you can even do it on all flights.
Also, I might be wrong, but I doubt the CO agent could see the SW schedule, last I knew, SW pulled their schedule out of the alliance system and now only SW agents can see it...again, I might be wrong on that one...
Anne