Given that in the census for Hiram K., his wife was named Nancy L., and that it is very easy to confuse H and K, it is likely that this 1849 marriage to Nancy L. Norberry is the record for Hiram K's marriage in Cumberland, Rhode Island. And it is likely, also, that his birth was in the same town of his marriage at age 24.
||Hiram H. Ballou|
||25 Nov 1849|
||Cumberland, Providence, Rhode Island, United States|
||Miss Nancy L. Norberry|
"Rhode Island Town Marriages Index, 1639-1916," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F8VR-789 : accessed 26 December 2017), Hiram H. Ballou and Miss Nancy L. Norberry, 25 Nov 1849; citing Cumberland, Providence, Rhode Island, United States, town halls, Rhode Island, and Rhode Island Historical Society, Providence; FHL microfilm 270.