Hi Rebecca I've just discovered this lineage of mine so don't have much on the Mays yet, but did find them finally in 1870.
They are in GREENE Co GA, Penfield, Dist 160. Page 435 (printed page)4 houses down from their son William Robert May and his wife Margaret and son Jasper (William Jasper).The name was incorrectly spelled on the census and so looks like "WARE"
Andrew May50They list everyone as b. GA but it's a " " Martha40so just another census error Elizabeth18Martha's age is a bit off Lavinia15 Alexander12 George9 Charles7(This is the J.C. on the 1880 Madison Census)
Sarah Elizabeth marries my gg grandfather William Hillsboro Jones.(but they marry in Franklin Co 1874).His parents are on the very next page on this 1870 census for Greene Co.His father was Sterling Washington Jones and mother was Martha Ann Swinney. Brother Charles is in their household.
I have a theory on the Elizabeth Smith on the 1860 Franklin Co census.After searching all of SC 1850 for Andrew May and family, I started going through the Anderson Co Census for 1850 page by page. Just in case they had completely mispelled their name again.I found a family with the exact right first names but with surname SMITH. Andrew, Martha, Frances and William. Ages are about right too.So, my theory is this - perhaps Elizabeth Smith is Andrew's mother but she was widowed from Mr May and then remarried someone named Smith.Could have been when Andrew was still pretty young, so then they mistakenly listed him as a Smith instead of a May on the 1850 census. Just a theory but it does kind of make sense.
You may email me directly at firstname.lastname@example.org