First of all, would there be an Irish name that could replace that of Solomon Grundy to fit in with this rhyme in Irish ?

Solomon Grundy, rug sé Dé Luain
Baisteadh Dé Mairt
Pósta Dé Céardaoin
Buaileadh tinn sé Déardaoin
D'éirigh sé níos measa Dé hAoine
D'éag sé Dé Sathairn
Adhlacadh é Dé Domhnaigh
Seo é an chríoch
Ar Solomon Grundy.

Corrections gratefully received, as usual - merci bien

I'd say it like this:

Solomon Grundy, rugadh Dé Luain é
Baisteadh Dé Mairt é
Pósta Dé Céardaoin (or: phós sé..)
Buaileadh tinn Déardaoin é
D'éirigh sé níos measa Dé hAoine
D'éag sé Dé Sathairn
Adhlacadh Dé Domhnaigh é
Sin é críoch Solomon Grundy.

And of course I can't comment on spelling as everybody knows how crap I am at that.

Ah well, at least I got some of it right. Merci beaucoup et tous mes voeux pour cette Nouvelle Année!

Merci, a toi aussi.

And you could replace Solomon Grundy with something like Seamus O'Lundy if you wished to give it a more Irish flavor

Thank you for your suggestion. I was thinking that perhaps it might be possible to turn the lines around a bit to give it a more typically Irish construction. Here's this example of what I have in mind, which might help -

Tá capall is cairt ag Seán Ó hAirt;
Tá bó agus lao ag Seán Ó Sé;
Tá peata uain ag Seán Ó Cluain;
Is sin é an fáth nach bhfuil orthu buairt.

Would Seán Ó Cluain rhyme with Dé Luain, for instance?