Dear Peg,Philippa noted several recordings in her message above:
Mná na hEireann has been recorded by the Chieftains, Sinead O'Connor, Kate Bush, Macalla, Seosaimhín Ní Bheaglaioch, Susan McKeown & the Chanting House, and even the Wolfe Tones. Kate Bush was well drilled for the pronunciation.
I'm sure you could do a search for these folks and find a recording of the song. Good luck!
-- Áine