I think the trick to that, and I could be miss-remembering, was to do it during a quest (maybe it was the tutorial?) hand. I think the first few you are guaranteed to win.
Note that I'm remembering this too from years and years ago, so I could be 100% wrong.
I learned my lesson during the Key To The City community challenge for GTAIV. Turns out once a save editor dropped, I found that one specific pigeon didn't spawn in my game. So, fuck rockstar.