PRONI is probably the 1st place to check for school records- and there are several different types. ED1 forms are basically the paperwork regarding the running of a particular school (inspection reports, etc.) and are interesting to get an overall history of a school but other than perhaps the name of a teacher there isn't much detail about people.
School registers are ledgers which record details of the pupils and in general have the following information:
child's name, age (later birthdate), number in register, date of entrance, address (townland or street in towns), religion, father's occupation. Sometimes they also list date child leaves school and what school they moved to or from).
PRONI's eCatalogue just put online today so you could try searching there:
www.proni.gov.uk/index/search_the_archives/ecatalogue.htm(if it's anything like their previous releases it might be difficult to get but just keep trying)