The first region-specific release in its Dreamland series, Putumayo's Asian Dreamland collection was released earlier this month with, yes, a collection of lullabies from Asia. Coincidence or not, it's one of the few areas of the world that Ellipsis Arts hasn't covered in its collections of world lullabies.
Although I keep an open set of ears when it comes to music, after more than three decades of listening to it, I've certainly developed some preferences, and one of those is a general indifference to music from Asia. I think it's perhaps the stringed instruments found in many Asian melodies, which may be relaxing to some, but not to me. So it came as little surprise to me that my favorite tracks on this 32-minute disk were those that downplayed the stringed instruments, such as "Cradle Song," from the Tatarstan artis Zulya, or "Aka Tonbo," a Japanese lullaby sung by Aiko Shimada and Elizabeth Falconer. Instrumentals like "Asadoya Yunta," which features a shamisen, a 3-stringed instrument similar to a banjo, were less pleasant to me. As slow as the instrumentals were, they would definitely keep me awak.
But one of the advantages of youth is that the ears of the young haven't developed their prejudices like their stick-in-the-mud dads, and so it's possible your kids will be incredibly relaxed by this collection. At the very least, it's a user-friendly collection of traditional Asian tracks supplemented by Putumayo's always helpful liner notes (you think I could identify a shamisen by myself?) A collection of lullabies, it's most appropriate for kids ages 0 through 6, though I'm sure older kids interested in traditional Asian music would find this a useful starter. Listen to Real Player samples here. Again, this collection is not for everyone, but if you're willing to try something new, Putumayo as usual offers you a good place to start.