I looked in the NSDAR Patriot Index and I did find a Amon Beebe. Is this your patriot:
Ancestor #: A008445
Service: CONNECTICUT Rank: PRIVATE
Birth: 5-7-1750 NEW LONDON NEW LONDON CO CONNECTICUT
Death: (ANTE) 1-21-1830 CLYMER CHAUTUAQUA CO. NEW YORK
Pension Number: *S49302
1) CAPT BEARDSLEY,9TH CO,
2) COLS WATERBURY,HUNTINGTON
Residence 1)City: NEW FAIRFIELD - County: FAIRFIELD CO - State: CONNECTICUT
2)X X WARSON
Children Listed: Amon Jr. and David
There is no Amos listed with the children. Do you have have a copy of Amon's pension records? If you like I can send you his pension papers. I have access to Heritage quest at my local library. Or a record from the New London CT that would list his children. Also there are several websites you can visit (paying ones) that have in their databases documents, newspaper articles,etc...
It is possible to obtain a copy of a DAR application under Amon Beebe. Use this URL for more information http://members.dar.org/apps/record_copy.cfm
Application papers of active, deceased, resigned, or dropped DAR members may be ordered for a fee of $10.00 per paper for electronic orders or $15.00 per paper for copies ordered by mail or by fax.
If there is anything else I can do please let me know.
This has been as a free look up service provided by a DAR volunteer.