My personal experience with my two kids living in the US is that I used to play Indian as well as Western classical(only classical)CDs all the time, to my first son from the time he was born. By 14 months, he started to prefer listening to Carnatic Music and by 2 years we was able to identify few ragas too. The best place to listen to CM as a family is the car! Since in the US, parents spend more than half of their time in a day driving the kids around for school,classes etc. I feel its the best place to listen and feel connected to music. Unknowingly it gets into their system. Now my older one is almost 7, he cannot spend a single day without listening to carnatic music. Once I got bored of repeatedly listening to a particular CD and for a change I switched to light rock....my younger one who was bearly 2 and half at that time said "I dont want this....can you please put PAAT(means paatu-carnatic song). Once I carpooled with another family dropping their son at school... and when I was about to park the car near his building and the American teacher was coming to my car to pick up the kid,
the boy said "can you please turn the Indian music off-thats what my mom does when we reach school"...I was taken aback!! I have never did that and my kids never felt that way! Infact my son sings "thripuresi Guruguha Janani" loudly when the same teacher came to pick him up couple of years back! He still does that! Playing carnatic music to the kids whenever possible, is a very effective way to get them interested in CM ...my two cents:-)