Redwolf wrote:
Also, if either you or your partner enjoy singing, that can be another way to help your child engage positively with the language from the very beginning. Music is powerful in that it engages both emotion and memory, and singing Irish lullabies, as well as "fun" songs as the child grows older (such as "Lámh, Lámh Eile") is a wonderful way to reinforce both your own and your child's language skills.
To get an idea of just how powerful music is as a memory aid, just think of all the people who, even as adults, find themselves humming the alphabet song when they're filing something or looking something up in an alphabetized list!
You DO NOT have to have the voice of an angel to do this...trust me! I hear "Oh, I have a terrible singing voice!" all the time from parents as an excuse not to sing to and with their children, and it simply doesn't hold water. Unless you're truly tone deaf (And tone deafness is actually extremely rare. If you can hum "Happy Birthday to You" or "Three Blind Mice," you are NOT tone deaf!), you can and should sing to your children.

But to help you out,
Ceol na Mara is absolutely gorgeous and I refuse to believe ANYONE who plays this to children and who claims not to end up singing along with it. For the record, anything that Futa Fata produces is worth buying - they are fantastic. Leaving a cd in the car if you have regular journeys with children is a great way of ensuring it is played regularly.
Ceol na Mara does not have traditional songs and rhymes, but has an entire cd of new songs about the sea and the characters who live there. Is aoibhinn liom é!

The accompanying words and explanations of phrases are very helpful for learners too.
http://www.futafata.ie/product_info.php?products_id=24
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Is foghlaimeoir mé. I am a learner. DEFINITELY wait for others to confirm and/or improve.
Beatha teanga í a labhairt.