This has been mentioned a couple of times here, but there hadn't been a thread on it. I know it as "Bluebird, Bluebird" or more commonly "Little Bird, Little Bird." Here are the lyrics I came up with for the Rise Again Songbook:

LITTLE BIRD, LITTLE BIRD

Little bird, little bird fly through my window (3x)
And buy molasses candy

Fly thru my window my sugar lump (2x)
And buy molasses candy

insert: chickadee, jaybird, whippoorwill, robin, bluebird, crow,
bobwhite, hummingbird

——trad. (Amer. play party song)

Players join hands in a circle & raise their joined hands to form windows. One or more birds in the center go in & out the
windows. At "buy molasses candy" bird stops at another player, who then goes to the center.

In American Folk Songs for Children (Ruth Crawford Seeger). On Pete Seeger Birds, Beasts, Bugs, & Little Fishes (as "Fly thru My Window") & Eliz Mitchell You Are My Little Bird.