I've contacted one of our group leaders. She said your bishop or stake president could request a group through LDS-FS or you could call LDS-FS and ask about a group. Groups are set up as needed and LDS-FS has the most direct contact with groups and leaders.
Here is the contact info for the New York LDS-FS agency (saw that you're from NY on your public profile, looked this info up on the
LDS-FS website):
LDS Family Services
NY New York Agency
217 East 87th Street, 3rd Floor
New York, NY 10128
PH: 212-876-7427
FAX: 212-876-1214
God bless,
Jiminy
PS - Have you checked online for a group in your area? If you haven't, follow
this link to do so.