You don’t say what denomination William was. Though St Saviour’s is Church of Ireland, that graveyard was used by all denominations until Kells New Cemetry opened in the late 1800s. However no denomination in Kells has any baptism or marriage records earlier than the 1830s (and those were RC records). The early COI records were destroyed in the 1922 fire in Dublin and the Presbyterian church has nothing before 1819. So it’ll be a struggle to find any church records relating to him or his parents.
The 1901 census for Kells lists 48 people named Parker. All but 3 were Presbyterian. So that suggests your Parker family were probably Presbyterian too.
The tithe applotment records for 1835 list John Parker in Kells townland and he’s the only Parker listed then.
PRONI have records of probate being granted to Thomas Parker in 1721, William Parker 1770 & Robert in 1834 (all of Kells). So it looks as though there have been Parker households in the area since the 1600s.
You could try searching the Registry of Deeds records for the 1700s in the hope that you find a lease, ideally a 3 lives lease, which could show the relationships between various Parkers. Originals in the Registry of Deeds in Dublin with duplicate copies on microfilm in PRONI, Belfast. (You would probably need to get a researcher to look them up for you).
