Back again. Here again is the marriage record previously posted for Alzinia's parents.
Vital Records of New Braintree, Massachusetts
Thadeus Cutlar Gilbert [int. Thaddeus] of Mansfield [int. adds Montgomery Co. New York] married Rebecah Redding [int. Reading] [rec. between April 1, 1803 and April 1, 1804] [int. Oct. 17, 1803]
Here's what I think this record means. Thaddeus Cutlar Gilbert is the spelling of his name when he filed his intention to marry. I believe the abbreviations mean he filed his intention to marry in Montgomery County, New York. He filed the intention on 17 October 1803. In the intention to marry, Rebecah's surname Redding is spelled Reading. This surname has many alternate spellings. (So does Gilbert, for that matter.)
Thadeus Cutlar Gilbert is "of Mansfield." There is more than one town called Mansfield, but I think this would refer to Mansfield, Cattaraugus, New York (not Massachusetts), since the Gilbert daughters were born in New York.
Alzinia Gilbert was born about 1805. Therefore, using this hypothesis about location, one might search for the birth record of Alzinia in Mansfield, Cattaraugus, New York.
Alternately Alzinia could have been born in Canandaigua, Ontario, New York; according to your research, she was married there, so she and her family likely lived there for some time. And just because Thadeus Cutler Gilber was "of Mansfield" when he married, it doesn't mean that he and his new bride moved there. On the link below, you can see the location of Canandaigua relative to Mansfield: http://en.wikipedia.org/wiki/Canandaigua_(city),_New_Yorkhttp://en.wikipedia.org/wiki/Canandaigua_(city),_New_York
Below is a link to Massachusetts Vital Records 1600-1849. I have not found the birth of Alzinia's mother Rebecah Redding on this site, but maybe you will. http://ma-vitalrecords.org/Surnames.shtmlhttp://ma-vitalrecords.org/Surnames.shtml
A last note: I admit I will be disappointed if you don't return to find the replies to your query. We responders would love to hear from you. That happens a lot - a person asks a question, we volunteers work hard to answer it, and then the questioner never reads the answers. Volunteer researchers are very patient about this situation and seem to believe that the research is worth doing regardless (someone else out there might be delighted to discover the posted findings at some later time.) But still - getting no timely response is kind of a bummer.
So that's it. I'll finish with this for now and await word from you.