Irish BMD indexes went online fairly recently, and you can find out more here:
Code:
https://www.irishgenealogy.ie/en/irish-records-what-is-available/civil-records
On the Search/Indexes page there's some Help on the right, with a link to how to order a certificate. This leads to a form which you have to post in, and you can order a photocopy for €4 (that's 4 Euros, in case it doesn't show up in some places).
The form doesn't include a formal space for parents' details, but I think it would be in order to include them.
The original (pre-online indexes) site with information about certificates is here:
Code:
https://www.welfare.ie/en/Pages/Apply-for-Certificates.aspx
This has a link to a form where instead of the €4 photocopy you can order a full certificate for €20. This form does have space to enter the parents' names and occupations, and they also ask for the kind of information you'd only know if you already had the certificate, such as exact date and place of birth. However, I've never had any problems with giving the information as found in the indexes - and as you'd send if you used the other form.
On the original site there's also a link for online ordering, but I've never used this and I don't know whether it includes the photocopies or just full certificates.
I believe you can also order from local register offices, as in England and Wales, but the only time I tried this I rang up first to see if it was possible, and clocked up a fair bit in call charges. Now that the centralised system is more streamlined I think I'd generally use that in future.
