Hi Belle
The age for James and Monica's daughter on the 1930 census is not 19/12 it is 1 year 9 months, which I have typed as it appears on the census 1 9/12.
1900 census
219 Hall? Street, Syracuse Ward 8, Onondaga, New York
Head, Jeremiah Keefe, born Feb 1870, age 29, married for 3 years, born Ireland, both parents born Ireland, imm year 1893, 7 years in US, Alien, Freight Dealer
Wife, Nellie, born Jan 1874, age 26, 2 children, 2 living, born New York, both parents born Ireland
Son, Francis, born Feb 1898, age 2, born New York
Daughter, Mary, born March 1899, age 1, born New York
If this is the family you are looking for then you will probably find that Nellie is in fact Ellen age 7 on the 1880 census. Nellie being a pet name for (H)ellen.
There is possibly a lot more info on this family but unfortunately I have to go out now. If no one else has found anything later, I will do more searches.
Best wishes
Agnes