The 1850 census would suggest Furman's parents were Henry and Frances Rickey of Morrisville, Bucks Co., PA. The 1860 census confuses the situation by having Furman with Samuel and Francis Rickey. When you check for Furman use the spelling of Firman for the 1850 and 1870 census records.
The 1850 and 1860 censuses would suggest Eliza's mother as Mary Stockton. Considering the close proximity to where Furman lived it is a strong possibility this is the right family. The 1840 census would suggest her father was Joseph Stockton.
You can look at some census records for free at labs.familyseearch.org and Ancestry.com. To view the rest check with your local libraries to see if they have Ancestry or Heritage Quest.
Beyond that you would have to check records at the Bucks County Courthouse. You might also try the Bucks County Historical Society which has an excellant genealogical collection.