This is from the 1880 census:
Year: 1880; Census Place: Howard, Howard, Indiana; Roll: 285; Family History Film: 1254285; Page: 341B; Enumeration District: 048; Image: 0024
Original data: Tenth Census of the United States, 1880. (NARA microfilm publication T9, 1,454 rolls). Records of the Bureau of the Census, Record Group 29. National Archives, Washington, D.C.
The link below will bring you to census data from 1850 onward, with children's names. Didn't find a marriage record for this couple.
https://familysearch.org/search/record/results?count=20&query=%2Bgivenname%3Anoah~%20%2Bsurname%3Acarter~%20%2Bbirth_place%3Aoh~%20%2Bbirth_year%3A1815-1820~%20%2Bspouse_givenname%3Alouisa~%20%2Bspouse_surname%3Aharrington~