One thing I was thinking was that she could ask to be given her tears? Like, for the rest of whatever period of time (maybe a set number of years, maybe the rest of her life), she won't be able to cry, because her tears will Belong To Nila.

Another potential option could be promising to make the Pledge to the Sorority, but that also involves being taken away to live in the Human Zoo in Elsewhere. May not be where you're looking Taurina, but it's there if you want there to be a more significant cost.