There were Parramores in Tyrrell County, from the 1700s into the 1800s. There's even a cemetery, Paramour Cemetery, in the Riders Creek area of Tyrrell (on the same road as the Malachi Chapel Baptist Church). There are no marked graves with that name, though.
If you go to the Tyrrell County, NC GenWeb site, you can find some Parramore marriages, and a bit of other information, but there weren't a lot of people there with that name:
http://www.ncgenweb.us/tyrrell/TYRRELL.HTM

By the way, Washington County was formed in 1799 from Tyrrell County, so a few families with that name did end up in Washington County, (Joseph and Thomas Parrymour), but by 1850, there was no-one in the census with that last name.