Sarah, It appears that my Park line may have also come from county Tyrone, but it is unconfirmed and I have not been able to access any information about them in Ireland.
I know there were many early Park's (or Parke) here in VA from Jamestown on.When did your's come to VA and where did they settle?Perhaps David was a sibling/cousin of my John (b: c1800).
This is what I think is correct: My Park's came to American in 1841, apparently arriving in NY and staying there for a few years.There was a John (the father), William (his son), and from I can see online there was another son, James.There may have been more sons and/or daughters arriving together.(William and his wife were married for over 50 yrs and had 12 children.Their son, Andrew, was born while they were in NY.)
I've concentrated on my line John b: IRE-William b: IRE-Thomas b: PA-Charles b: VA-Charles b: VA-me b: VA.
I located John and William in/near Springfield township in Mercer Cnty PA on the 1860, 1870, 1880 census'.In 1900, William is on the census in Chesterfield Cnty VA as is my great-grandfather Thomas.I don't know when they actually came to VA but I know Thomas was married in Chesterfield Cnty in 1889.Another of William's children, Andrew, was also in Chesterfield Cnty VA.
I wish I could help you more.I just recently gathered the information I have, after locating the marriage record for my great-grandfather Thomas.I will say, though, when you search for Park on the census' make sure you check every possible variation and spelling. I've seen Park, Parks, Parke, and Parkes.