Lá breithe sona, with short e (not bréithe).
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I've also seen "Breithlá sona duit"...not sure if it's Béarlachas or not, but it seems to be quite popular.
to me it's a Béarlachas (calque of "birth+day"), because in Modern Irish you don't prefix nouns to nouns, you put them one after another, the second being in the genitive and defining the first one. Prefixing nouns is a very old thing that has disappeared in "natural" Irish (and being used again by those who invent new words in offices, because they think in English, I guess).
Quite popular maybe on the internet, I guess it's because "breithlá" is exactly like "birthday" so it's easy for English speakers (but does Irish need to be like English?)... But I think somone who had only Irish 100 years ago would never have said something like that...
Some write "Lá breithe s
hona", which is wrong because lá is masculine singular nominative (doesn't lenite, then) and anyway breithe is feminine singular genitive (doesn't lenite either). So no reason to lenite "sona". But even knowing that lá is masculine singular nominative is enough because it's the day that is happy.