Waterford birth and marriage records are online with a not for profit but fee paying website. You should easily be able to find a birth record for Mary Phalen, as you already have the marriage. A birth record will give you where in Waterford she came from. County Cork is also partially with the History Foundation - but just the north-east portion so if he was born there his place of birth will also be listed on his birth certificate.
In 1851 there were no Phelan listed by the name of John but 281 Phalan's of these 41 named John and over 1000 Walsh, no Welch. There are 21 Daniel Fitzgerald's and over 1000 Sheehan's. www.failteromhat.com
For further resources please refer to:www.censusfinder.com