Hi, I don't know if this answer is too late - the original post was in February - but I will do my usual thing of warning against imposing the cultural assumptions of English on Irish. In other words, the rhyme about Monday's child is full of grace is really well-known in English but not in Irish and the word Aoine means "fast, abstinence".
If you had asked me a week ago, I would have said that there is no equivalent to this rhyme in Irish. However, I did check a book by Nicholas Williams called Cniogaide Cnagaide, which is a compilation of nursery rhymes and children's verses in Irish. According to this, there is an Irish version of it (though it doesn't rhyme) which was collected about seventy or eighty years ago in Co Galway. It is Naíonán na hAoine - Is glas í do shúil agus croí na féile i do lár agat (Child of Friday - Your eye is green/grey and there is a generous heart inside you).
In case anyone has this book and finds that my version differs from it, for some reason the book has Naíonán AN Aoine, but this is clearly wrong, and doesn't match Naíonán na Céadaoine and Naíonán na Déardaoine in the same verse, both of which are compounds of Aoine, so I have corrected it.
However, my word of caution still stands. This rhyme is quite obscure and hardly known among Irish speakers.