searching for adopted cousin

You could register your details with the National adoption contact preference register. There's a small chance he may have registered and details would be matched. It would be handy if you could pinpoint his date of birth. If you are near Dublin you could go to the General Register Office in Werburgh Street and look up the birth register for his month/year of birth. As you know his name and obviously mother's maiden name, it should be easily found. With his exact date of birth you could then look up the adoption register and get records of baby boys with the same date of birth. Problem is you may find a few but it would be a start.