Sounds like everybody has you covered on screwing the 2by so it is screwed into a stud on either end of it which would be about 16" or 24" depending upon how far apart they put cripples in above the header.
Unless you have a skyhook, you probably need to do a ceiling mount as was suggested, go to the hardware store and buy some of that light weight angle iron that is already predrilled with a hole every inch. It doesn't hold much weight. You need two pieces to run up to the ceiling (about 5' long each) and then another piece long enough (about 3' long) to span two ceiling joists which are probably spaced at 24". Get some bolts to fit the holes. Cut the risers going up so the opener is level. Just let it rest on the open door. The risers don't necessarily have to go straight up but can angle out a ways which may avoid some cutting. The opener will have bolt holes or may need a short bracket. Look at how your garage door rails are held up.