I don't have info about the parents--am also looking. However, the dates you listed (1784-1854) are actually the birth and death dates for Frances Muse--John Rice's mother. John Rice had to have lived longer--I have info about their children which were born as follows:

Fannie Muse 4/4/1859
Mary Eugenia 7/22/1860
Harriet Healy 11/29/1861
William Ashton 4/18/1864
Oscar Roan 4/24/1867
George Thomas 4/16/1872