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DISCLAIMER: I know zip about rugby, Australian rules football, or the various soccer organizations so I disregarded those going in; not going to venture into areas with which I'm unfamiliar. Hence this discussion's scope is confined to North America.
Anyhow: pretty much what the subject line says. A few items:
Of the twelve NFL teams at the beginning of the 1950s, only the Philadelphia Eagles and Green Bay Packers used green.
None of the original eight AFL teams did, but the Jets adopted green when they changed from the New York Titans for the 1964 season.
Of the nine CFL teams before the Ottawa Rough Riders folded, only the Edmonton Eskimos and Saskatchewan Rough Riders used green.
NONE of the NHL's original six used green (three-Chicago, Montreal, and Detroit-used red or a close variation of it; two-Toronto and the Rangers-used blue; one-Boston-used black).
NONE of baseball's original sixteen teams used green in their original locations (although the A's adopted green while close to the end of their tenure in Kansas City, and for a very brief period in the '30s, the Dodgers called themselves the Aces and used green and white uniforms)
I don't pay attention at all to the NBA, so the only one I'm aware of is the Dallas Mavericks.
And even today it's not used much. In baseball, it's the A's; the NFL still has the Packers, Eagles, Jets (no, turquoise doesn't count); the NHL has the Stars and Wild (both expansion teams; teal or turquoise don't count).
So...how would one or more teams adopt green for good back in the '30s, '20s, or before?