If I debate with theists, I tend to use "your god" or "the god of christianity". This way, I can avoid making them think that I acknowledge that their god "is THE God", but that I am just denying it. I de-throne their god and toss it into a clusterf*ck of other mythological beings.
I notice sometimes that other atheist debaters capitalize the word god, and I feel that the theists believe that this only confirms their gods' status. If we confirm their gods' status, then we are just rebels. How do you use the word "god"?