It may be easier said than done to find public information about Ossetian lullabyes. From my perusal of ossetians.com and wikipedia, it is an historically patriarchal society where women are traditionally not heard in the public sphere. While that is reported in some articles at ossetians.com to be changing, there seems little on the internet to show that is so, while said web pagesalso state that such liberations are generally frowned upon by a lot of Ossetians; the authors say that modern social freedoms are to be dialed back to as not to offend Ossetian tradition. At least that what's I took away from the articles I read.

The list of types of Ossetian music shown on wikipedia was made by a male. It does not acknowledge any music specifically for children, perhaps because traditionally it is shameful and taboo for men to participate in that sphere. It may be that such music must be found directly from the women who know and it, or it may be that babies and kids are sung to sleep with historical and other folk songs, not infantilized to the degree we see in North America.

About the song link provided by unnamed GUEST: What is thought to be suitable for kids in 21st century North America ain't necessarily so elsewhere and else-when. Think Grimm's Fairy Tales for an obvious example, and I wonder how many kids of the British Isles not to mention early Appalachia or early Mexico or the wild west were sung to sleep with heroic war songs or love ballads or cautionary songs.

With that in mind I'm thinking about the Shepherd of the Black Mount linked-to above. If the lyrics are politically acceptable for this project, I wouldn't necessarily rush to dismiss it on the grounds of too much vigour. On purely musical grounds what you hear as too much vigour is to me simply a result particular arrangement and recording: Those voices (other cultures have different sounds that are considered desirable), the chord progressions, and the busy accompaniment. Imagine the same verse-melody in your own voice along with sparsely-plucked guitar, and for the chorus your voice plus a couple of lower or higher ones "ooo-ing" notes from the chords and/or descant-y stuff (with or without guitar. Just a thought...

Whatever you end up doing, it appears that you have taken on quite a task for which I applaud you, and I wish you every wonderful success! I do hope you'll post a link to the result.