Local Controller described conflict with 2 successive departures; requiring the use of visual separation; claiming fatigue as a causal factor of the incident.

Narrative

The A319; a departure off Runway XXL; issued immediate right turn heading 100 degrees and switched to Departure Control. The Departure Controller issued a northeastbound turn to the A319. The next departure; the CRJ; flew runway heading to 1.5 NM; then turned right heading 100 degrees. Since the A319 had been issued an immediate right turn to 100 degrees; and the CRJ flew runway heading for the first 1.5 NM; as the CRJ turned right the aircraft flew toward the A319; which by now was climbing through approximately 4;500 FT MSL. The CRJ was approaching about 4;000 FT MSL; climbing to 5;000 FT MSL; and was approximately 2 miles west-southwest of the A319. Since the CRJ was still on my frequency; I issued traffic to the CRJ; which indicated they had the A319 in sight. I instructed the CRJ to maintain visual separation with the A319 and switched the CRJ to Departure Control. I was busy at the time; with numerous arrivals on both Runway XXR and Runway XXL; numerous arrivals on my frequency taxiing to hold short of Runway XXL; and several departures waiting. I slept only about 5 hours the night before; and feel that fatigue played a factor in this event; as I fell behind rapidly and basically forgot about the CRJ; which was turning and climbing toward the previous departure. I am not as young as I used to be; and need to ensure that I get needed rest before I report to work. In the future; I will strive to get the sleep I need before reporting for work.