Do you know what religious denomination your Archbold/Headon couple were ?
The only Catholic Michael Archbold marriage I see around this timeframe is to a Catherine Kelly in St. Mary RC Dublin City. Not very many Catholic parishes have records going back to the 1700s or even the early 1800s, so it's possible there's no written record available for a marriage of your Michael and Bridget.
Records for other denominations, e.g. Church of Ireland, Presbyterian etc, are not as well covered online so searching can these can be more difficult without knowing a more detailed location, e.g. the name of a town or parish in County Kildare. I tried a quick search of the additional non-Catholic records online but did not see any promising matches.
A genral search of baptisms shows several Bridget Headon/Haydon baptisms in various parishes around County Kildare, Kilcullen 1795, Athy 1811, Castledermott 1802, Castledermott 1802, Castledermott 1804. Castledermott RC parish happens to be one that has early records going back to 1789 - most of the other parishes nearby have records starting much later e.g. Narraghmore 1827, Baltinglass 1807 etc, so the results we are seeing are only a small sample of those baptizesed in the area around that time.
Do you have any other clues that might help - e.g. names and dates of any children born in Ireland ?