Hi Maz
Welcome to Rootschat -
You might like to have a look at this site -
http://mayo.brsgenealogy.com/index.php?&set=yesThe Irish Family History Foundation are putting many of the parish records on line.
It's free to register and search but costs five euros to view each record.
If you're looking for a birth/baptism you can also put the father's name in so it narrows the search a bit. Unfortunately it doesn't give the parish so it's sometimes a matter of trying each parish from the list.
There are a few birth/baptism entries for Isaac Beckett but only one with a father Archibald (in 1864) - parish is Westport District? .
Hopefully the record might give the mother's name.
You can try different children with the father's name as Archibald.
There's a baptism of an Archibald Beckett in 1822 (Thurlough Church of Ireland) and a couple of later burials.
One of the drawbacks of this site is that you could potentially waste money if it's the wrong record as there isn't a lot of additional information to help you choose the right record - especially if you have more popular names to look for - like mine!!
I think the site suggests putting 40 euros on the account but you can put less.
The link is for County Mayo but if you want to try other counties - click on 'map.'
Here's a link for Griffiths Valuation of Ireland - just select Mayo and search for Beckett - there' are a few entries .
http://www.failteromhat.com/griffiths.phpYou might already have this link -
http://www.leitrim-roscommon.com/1901census/census.shtmlHope this is useful.
Good Luck
Neptune