Just to update the first post, EI is twice daily - 2 to DUB, 1 of which is via SNN.
I was going to change it when I found out, but I figured that someone would point it out.
Here are more airlines listed at the JFK
page, although I am not sure about some of them.
Aero Mexico (I know they fly in)
AeroSvit Ukrainian Airlines
BWIA (I know they fly in)
Lan Chile (I know they fly in)
Saudi Arabian Airlines (I know they fly in)