Statutory birth registration did not start in Ireland till 1864. Prior to that you have to rely on church records (where they survive). To do that you need to know the family?s denomination.
You say that the family attended church on Saturdays where a travelling Wesleyan Minister preached. That points to Methodism. However you also say they are buried in Drumlee Presbyterian Churchyard. That points to Presbyterianism. To make matters more complex, if they were Methodists, then you need to know that Methodism was not established as a separate denomination in Ireland till much later than in England, and so in the 1820s, most Methodists still used the Church of Ireland for sacraments (ie baptisms and marriages). So without any additional information, I would advise you to search the Presbyterian, Church of Ireland and Methodist records in the areas where the events you are interested in occurred. Copies of most surviving records are held in PRONI in Belfast. Most are not on-line and so a personal visit is required to access them.
Looking at the 1901 census for Co Down, most of the Magarey/Megarry families were Church of Ireland, but a few were Presbyterian or Reformed Presbyterian (ie Covenanters). I didn?t see any Methodists.
Ballykillibegs is probably Ballykilbeg, which is a townland in the parish of Down. You can see what records survive for that parish on the PRONI website.
Roden/Clanbrassil estate papers are probably deposited with PRONI. (A search on the ?Earl of Roden? brought up 166 matches, on the PRONI site. ?Clanbrassil? brings up another 119). Again a personal visit is required to search them.
School attendance records are also deposited with PRONI but you need to know the exact school, and there aren?t many records before 1850.
I can?t find a townland called Fofarry in Co Down. There is Fofanny (to be exact Fofannybane and Fofannyreagh) both of which are near Kilcoo. I don?t know of anywhere named Tolamin Park.
http://www.proni.gov.uk/
Drumlee Presbyterian church is in the parish of Drumgooland. PRONI have the following records for that church:
P. Drumlee Baptisms, 1826-1980; marriages, 1845-1920; session minutes, 1826-54.
