Family letter and IGI etc. FamilySearch couldn't find her in 2017 even with birth range 1795-1825. However, that was for "Grace". With date and alternative name from tombstone, we may have more luck getting a birth record.
Other children included several who died young. Marien became Mrs Lyons and (according to mid-20th-century letter) had children Will Lyons, Samuel Lyons, Robert Lyons, Janet Lyons, Jean Lyons, and Annie Lyons, but the 1880 census doesn't quite match that list. John - 1860 census and 1870 census - was said to have had children Robert Swan, Grace Swan, Mary Swan, Annie Swan, Janet Swan, and John Swan" close match with 1870 census.
1850 census shows a bit at number 1052:
Allegheny city, ward 3, Allegheny, Pennsylvania - very faint, and transcriber didn't try hard enough, but clearly "Swan" to this researcher and to at least one FamilySearch index