Enroute Controller described a conflict event when dealing with bad ride requests. The reporter failed to observe the conflict developing.

Narrative

Working Sector X; a B737-400 asked for higher due to a bad ride at FL330 after he heard another aircraft asked and was issued FL350. He was issued FL350 and became uncomfortably close to a B737-900 at FL340 during his climb. I noticed it just before the Conflict Alert began. I attempted to issue a turn but was told by the B737-900 that the traffic was 200 FT above him. I asked the B737-400 to expedite and report level. He notified me that he had 400 FT to go and I simultaneously measured 5.9 miles. The next RADAR update showed FL350 with 4.3 miles of separation. The biggest lesson learned is DO NOT let your scan deteriorate; especially with only one set of eyes and aircraft wanting different attitudes because of bad rides. I should have double checked to make sure the altitude was clean and at the very least told the B737-400 to expedite to the altitude he wanted because first glance there was no aircraft near him. Anything would have helped in this situation; from having a D-Side to looking at the URET for red 1's after entering the altitude. The thing that concerned me is that the Conflict Alert did not engage until after I recognized the conflict. It actually went off when the two aircraft where FL340 and FL342 head on.