This men's adult soccer league has been in existence since 1976. The Leagues name is:

Long Beach Men's Soccer League and is usually known by LBMSL
It is based in Long Beach California.

I envisaged a net slung between two palm trees and a setting sun.

OR

6 inter-locking rings, in a pyramid formation.
The top ring enclosed the year (1976)
Two rings below this enclosed the letters L and B
and the three rings below them enclosed the letters M,S and L.
I thought the rings and letters should be white and the area inside the rings (grass) green. To sort of represent the white lines on a soccer field.

However, what the hell do I know, you're the graphic designer - come up with something of your own and if it's better than my suggestions - I'll be happy to go with it.