Hi,

Prior to 1892 all vital records were originated and filed with the Town/City Clerks. You can do a Google search for the clerk in Buxton and ask about his birth record.

1840 Corrina, Penobscot, ME
Joseph A. Paine

1850 Greenfield, Dane, WI
Joseph Payne, b. ME, 48
E. M., wife, b. ME, 41
Elisxabeth A., b. ME, 18
E. A., dau, b. ME, 16
J. S., son, b. ME, 14
John E., b. ME, 12
W. F., son, b. ME, 10
M. M., son, b. ME, 7
Charles A., b. WI, 5
E. M., dau, b. WI, s

He probably died in Dane County. I don't know if Wisconsin was tracking deaths that early nor not. You can do a Google search for Dane County Genealorigal or Historical Society and ask them if they have a local death index, indexed newspaper death notices and inventories cemeteries.

1860 Fitchburg, Dane, WI
Eliza Paine, b. ME, 50
Eliza, b. ME, 26, school teacher
John, b. ME, 28, farmer
Wilber, b. ME, 21, farmer
Mary, b. ME, 18, house keeper
Charles, b. WI, 14
Ellen, b. WI, 12
Flavius, b. WI, 8

1870 Fitchburg
Eliza A. Paine, b. ME, 60
Charles A., b. WI, 24, farmer
Ellen M., b. WI, 20, teaching school
Flavius, b. WI, 17, farm laborer
John W. Gager, b. WI, 10
Mary E. Merrick, b. WI, 37, teacher

1880 Fitchburg
Eliza Paine, b. ME, 71, widow, farmer
Ella Rose, dau, b. WI, 30
Ebbin, sonlaw, b. Nova Scotia, Can, 37, artist

Eliza probably died before the 1900 Census. Successful Searching!