This isn't my family but I have searched for others in the Little River, Wake Co. area and found that over the years these families drifted back and forth between Wake and Franklin Counties, apparently an area close together. In addition, my families did not seem to attend much school, so their ages varied greatly in the censuses. I then looked quickly in ancestry to see what I could see for Joseph D. Pulley. There are several Joe Pulley born 1855-1865 in NC. If you are looking for the Joseph D. Pulley who married a Sarah/Sally, his death certificate seems to be in Northampton Co. in the County hospital with burial taken care of by the county. His death certificate reads J. David Pulley. However, after searching again in the North Carolina death certificates available on ancestry, I think you may be looking for the man whose death certificate reads Joe Turner Pulley, 88, born 10 Jan 1858 Wake, died 10 Dec. 1946, Wake Forest, Wake. Spouse: Ellen W. Pulley; Parents: Joe Pulley and Fanny Pearce. If you have an ancestry subscription you can find this family in at least the 1860 and 1870 censuses, I believe both times in Wake Co. I didn't look further for him.
Good luck in your searches.