There are a few basic Christmas greetings here in the three main dialects.

http://www.gaeilge.ie/UsingLearning/sou ... t.asp?id=7

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"Connacht" is the genitive form... should be "Connachta" in their table (and it's an official site... ). And I'd say Mumhain is a dative form.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

A Lúghaidh, Múmhain is like muintir, aimsir, namhaid, tigh and many other nouns where the erstwhile dative is the correct nominative in Munster. Múmha was the nominative several centuries ago... Of course, the problem is that which nouns have generalised the dative varies from province to province, e.g cara in Munster, caraid in Connacht etc.