PRONI will do simple searches for you. They won’t do lengthy or trawling research. So you would need to ask them whether they will do your research and for a quote, and as has been said you need to pay in advance whether they find anything or not. Their fees are on their website but it’s something like £16 per 15 minutes. You would normally find it cheaper to use a commercial researcher. (There is a list on the PRONI site).