William and Matilda's marriage took place in the Church of Ireland St. Catherine's - there's also a Catholic St. Catherine's in Dublin city.
Unfortunately marriage records from that timeframe dont include much detail, just the date, names, their current residences and names of witnesses, and no details of father's, so very few clues to start a search further back. Sometimes the witness names can be clues, as they are often related, but in this case neither have the same surname as either the bride or groom.
Did William and Matilda stay in Ireland ? did they appear on any census returns ?
In some countries death certs can include details of parents, so might be worth checking out...
Currently Church of Ireland records are not as well represented online as Catholic records and coverage is very patchy, so making a baptism search difficult, as it's difficult to prove, or rule out, any potential records located. In addition there's also the problem of parishes where historic records have been lost, so cannot be searched. A search of the irishGenealogy website shows on possibility that's worth noting - a William Hall baptised 27th February 1784 at St. Catherine's CofI, so the same church and parish as that marriage. The residence is recorded as 'Chambr St' - likely Chamber Street, and the parents as William and Mary. Maybe a little old to be your William, but given the same street , first name & surname, possibly related ?
A search of Dublin directories for any details on Chamber streets shows another possible connection - Wilson's Directory of 1804 (part of the Treble Almanack) there's an entry for a William Hall or 35 'Chambre Street', occupation Dyer. Do you know the occupation/trade for your William ?
By the mid 1800s the surname Hall appears all over Ireland, but was much more concentrated in Ulster counties, with Antrim, Armagh and Fermanagh at the top of the list.