I doubt Geneseo does because from what I hear its in the middle of bumdumbdiddle no where. But BU has had a team in the past, I don't know the depth or extent of what they were but two of my friends played for them when they did. PM me and I can put you in touch with them.
Binghamton had a club, but I believe that they weren't funded by the university. The only two suny schools that are really competitive are SUNY Buffalo and SUNY Oswego. Both are funded by their respective schools and have winning programs. In fact, UB won the national title in 2011.
LET ME WIN, BUT IF I CANNOT WIN LET ME BE BRAVE IN THE ATTEMPT
It has been made official that under no circumstances should the male have to pay for birth control