B737 Captain describes the circumstances surrounding a fatigue call that resulted in a flight cancellation.

Narrative

I called out fatigue after completing a cross country deadhead to LAX just before operating a 'red-eye' from LAX back across the country. I was immediately placed in 9 hours of rest and the flight was eventually canceled and delayed until the next morning. For the month; I am scheduled as a Reserve Captain. For the past two weeks I have developed a sleep cycle to prepare for early morning assignment notifications. I typically go to sleep at 2100 and wake up at 0600. This sleep cycle continues on my days off at home. I received a flight assignment to report at 1920 on Day 3. I was to 'deadhead' to LAX; then operate the 'red-eye' from LAX to ZZZ1. I was notified of this assignment on Day 1. On Day 2; I completed a flight assignment from ZZZ2 to ZZZ1; and returned to ZZZ2 at 2330. I went to sleep at 0030 and woke up Day 3 morning at 0730. Activities during the day included exercise; rest; and eating. I attempted to get some sleep prior to reporting at 1920 for the deadhead to LAX; but was only able to get a one hour nap in from 1500-1600.The company must develop a fatigue risk mitigation program to avoid scheduling pilots multiple legs in a single duty period schedule to span the hours of 0200-0500. In addition; the Company should avoid assigning early morning reserves (0400-1800) pilots to conduct 'red-eye' or Continuous Duty Overnight (Stand-ups) events. As for preparing for a red-eye; the Company should stage pilots at the originating location of the red-eye to provide ample opportunity to obtain sleep just prior to reporting for the 'red-eye'. A 'Red-eye' flight should be a stand alone event without a preceding 'deadhead' or operating a leg just prior to the 'red-eye'. Plus; pilots should not be scheduled to operate flights immediately after completing a 'red-eye'.