There are only a handful of Paisleys in the Freeholder Records which dates from about 1817-1830 (the time that your William/James lived there). There are a Hugh, James and John in Ballyblack (Co. Down), a John in Whitespots (Co. Down), a John in Ringbane (Co. Down), a Robert in Currard (Co. Fermanagh), a William in Ballywitticock (Co. Down), and a William in Creemore (Co. Armagh). There are none listed in Co. Antrim.
Why do you believe Co. Antrim to be the place they came from?In the Surnames in Ireland (Ancestry.ca), variations of the name are Pasley, Pazley, and Peasley. In the distribution of surnames in 1890 (much later than your crowd), the name is most commonly found in Dublin & Co. Antrim.