BOB,
It depends what you are talking about. Morning doves are the light gray or brown bird commonly hunted in the south and midwest over sunflower fields. You cannot shoot those in NY. Rock Doves, or City Pigeons are the charcoal gray colored birds with red and green metallic heads. As long as you have a small game hunting license, you can blast away all day at these with no bag limit. I must stress though, and many people don't realize this, you HAVE TO have a license. Its just like hunting woodchucks.
Good Luck
Rob