I've not timed it, but a hummingbird seems to appear about once every 10-15 minutes. Follow it carefully and take careful note of which flower it stops at. Once it has flown away (not before) you can drop a peep on the flower to collect it for the lei.

TIP 1: Use kids rather than adults as they run faster.
TIP 2: Don't try to pile all the kids at once onto the flower. They'll quite likely start a jumping or racing contest instead. Wait until one starts moving away before dropping the next.
TIP 3: Don't pause the game, at least in the current version. Version 1.00.01 has a pause-related bug that might mean that the game will crash and you'll lose up to the last 10 minutes.