The Barnum Family, 1517-1904 says that he had a daughter.
In the 1880 US Census for District 35, Binghamton, Broome County, New York the family of Hiram Barnum was enumerated as follows:
Dwelling #32; Family #42
Barnum, Hiram; W; M; 37; Married; Fire insurance representative; b. New York; Both parents b. New York
Barnum, Jennie; W; F; 28; Married; keeping house, b. New York; Both parents b. Scotland
Barnum, Agnes L.; W; F; 6/12; b. Dec; Daughter; b. New York; Both parents b. New York
Murray, Kate; W; F; 17; Servant; Single; b. Pennsylvania; Both parents b. Pennsylvania