How can I apply for my son's Non-O visa while in Ireland, and what are the requirements?

You have to talk with your employer about the procedures/documents to apply for your baby's visa, especially if you are going to do it inside Thailand.

There are companies that don't (or cannot) support employees or family members if they are overstaying or illegally staying in Thailand for their own reasons.

Better be careful to think no problem for children to be overstaying, especially if the main applicant is a Non-B holder.

1- 𝗜 𝗰𝗮𝗻𝗻𝗼𝘁 𝗮𝗽𝗽𝗹𝘆 𝗳𝗼𝗿 𝗶𝘁 𝘄𝗵𝗲𝗻 𝘄𝗲'𝗿𝗲 𝗶𝗻 𝗕𝗸𝗸,

Correct you cannot get a visa from a thai consulate in another country when you're not IN that country.

𝗚𝗼𝗶𝗻𝗴 𝘁𝗼 𝘁𝗵𝗲 𝗰𝗼𝗻𝘀𝘂𝗹𝗮𝘁𝗲 𝗶𝘀 𝗮𝗹𝘀𝗼 𝗻𝗼𝘁 𝗮𝗻 𝗼𝗽𝘁𝗶𝗼𝗻

Correct again, NO consulate has walk up service anymore, and all applications for thai visas are done online thru the eVisa web-site once you're in the country of the thai consulate you're going to apply for the visa thru

𝗰𝗮𝗻 𝗜 𝗮𝗰𝘁𝘂𝗮𝗹𝗹𝘆 𝗮𝗽𝗽𝗹𝘆 𝗳𝗼𝗿 𝗶𝘁 𝗮𝗻𝘆𝘄𝗮𝘆 𝗯𝗲𝗳𝗼𝗿𝗲 𝘄𝗲 𝗴𝗼?

NO you can only apply for a visa to thailand thru a thai consulate once you're OUT of thailand, and IN that country.

To be completely honest;

There is almost NO reason to jump thru the hoops getting a super young baby a Non-O from a thai consulate before you come back then doing the additional hoop jumping to get them the matching extension based on being immediate family of someone legally working here on a Non-B visa/extension.

Just bring them in visa exempt and let them overstay. At least until you're going to send them to school. I know foreigners with young children here on multi YEAR overstays and nothing happens to them or the parents.

The fines for overstay don't start until the child is 15 years old and the banning for overstay doesn't start until they're 18

Don't get me wrong, it's totally okay to get a 90 day Non-O based on "staying with non-Thai family" from the thai consulate online when you're out of the country before you come back

BUT

There is no real reason to do that, especially for such a young child

As far as getting the Non-O visa inside the country after you're back (if you can't do it online when you're out of the country in Ireland via the consulate in London)

Just bring them back in on their passport visa exempt, go to the immigration office that issued your Non-B extension and apply for first the 90 day Non-O visa for 2000baht and then 2 months later the matching extension that piggy backs off yours