The genitive of rí is rí, but being masculine the article stays as an.

The genitive plural of géillsineach is géillsineach, i.e., it reverts to the singular form.

Ar son an rí agus a ghéillsineach

(@kk, etc., do we need to repeat ar son in these cases, like we do the preposition?)

(I really think do is fine here though - that way you don't have to bother with the messy genitives. )

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Nope. Parallel genitives are perfectly fine. In fact, if you repeat the head noun, you run the risk of changing the mean. In this case, the change in meaning would be negligible, if there at all, but if it’s a regular genitive, you might create two things owned instead of one. Compareteach mo mháthar agus m’athar with teach mo mháthar agus teach m’athar—one of them implies a divorce, while the other doesn’t!

So even if compound prepositions are often considered prepositions, they act here as what they really are: preposition + noun constructions being ‘owned’ by the object of the ‘preposition’.

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Not a native speaker.

Always wait for at least three people to agree on a translation, especially if it’s for something permanent.

My translations are usually GU (Ulster Irish), unless CO (Standard Orthography) is requested.

Good point. Thanks for the clarification.

And does the version with do carry the meaning without resorting to ar son, do you think? I'm pretty sure it does. (Bríd, any opinion on that?)

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Are we sure the meaning intended is "For the King and his subjects"?
Seems to me it could be a third party referring to the King and seperately the People.
Just wondering.

"Pro rege et grege" is the Latin.
As well as being the Motto of the Pattersons it is also the motto of The Royal Danish Life Guards (in your court Koko )

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It is recommended that you always wait for three to agree on a translation.
I speak Connemara Irish, and my input will often reflect that.
I will do an mp3 file on request for short translations.
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They have a motto?!

I didn’t even think they were allowed to talk!

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Not a native speaker.

Always wait for at least three people to agree on a translation, especially if it’s for something permanent.

My translations are usually GU (Ulster Irish), unless CO (Standard Orthography) is requested.