When looking at Civil records for the area the registration district(SRD) is Swineford which is further partitioned into what are known as dispensary districts. The dispensary districts For Swineford are Foxford, Kilkelly, Kiltimagh, Lowpark and Swineford.
People from the Kilmovee area would more commonly associate Ballaghaderren ( part of Roscommon from 1898) as their primary centre of population and when they left they would use Ballaghaderreen on mail as this was the centre from which their mail was distributed. Such is the connection to Ballaghaderreen, Roscommon today that a large part of the parish have Roscommon Eircodes (postal/zip codes) rather than one for Mayo.
I would look for a connection for the Lavin people of Clooncarha with Kilkelly by way of land transfer (
http://www.valoff.ie/en/Archives_Genealogy_Public_Office/ ) or marriage into the townland as the Lavin name is not present at the time of the Griffith valuation.
A Michael Lavin and Mary Leech of Kilkelly had a daughter Mary in 1859 and by virtue of location may be a connection to your John. The earliest births for a Lavin/Lavan connected to the townland Clooncarha appear about 1864 and the earliest marriage was again 1864 for a Thadeus Lavan to a Catherine Hopkins which may support the view that they moved into the townalnd between 1856 and 1864. I would also be very flexible with you birth year reference from the census. Dates of birth/ages were at best estimates as they were rarely the preoccupation they are today.
As for School records the only records which have been microfilmed in the parish relate to Clooonamna School which falls between Kilkelly and Clooncarha and would not have drawn children from either area.