Family And Home
This site has all kinds of good resources and links to support groups. No specific support groups for this organization.
Mothers of PreSchoolers is a group for moms with a somewhat spiritual focus, but according to their website they welcome all moms. There is a group in Simsbury.
National Association of Mother's Centers
NAMC provides local support groups, there is one in Avon.
Moms clubs have local support groups, no religious affiliation.
Attachment Parenting International
Based on the Attachment Parenting theory by William Sears, these groups encourage baby-wearing, nursing, co-sleeping, and other child-friendly practices.
Mothers and More
Mothers and More has local support groups, to help women to move from careers to home.