If you have a Weber Grille (dome type) you can do this. This is not a true form of smoking, but its darn close.

I mix up my favorite marinade and add a wee bit of smoke sauce. I inject about 1 cup of this directly into turkey breast, leg etc. I soak a large bowl of smoke chips at least 24 hrs. Place a round diposable aluminum pan in center of grille. Fill it with water or a flavored broth. Build your coals around this pan and along inside edge of grille. I cook Turkey until internal temp is 160 Deg. About last hour of cooking I throw in the smoke chips. The turkey turns a golden brown with definate smoke flavor thru out. The pan of water along with the injection makes this the moistest turkey you'll ever lay your lips on!! I cook 2-3 like this every year.