Anzili
There is not a lot about her unfortunately. From the little that's out there, I would assume that she is associated with childbirth and possibly fertility (of the land and/or of people). Her name was sometimes written with the Sumerogram "Ishtar" so, unless that's typical of all goddesses, it might not be a stretch to say that Anzili and Ishtar have similarities.
Her consort varies by region, but the two I've seen attested are both weather gods. In Kulisisna, she was worshipped alongside their weather god and Innara (god of woods and fields). Perhaps she is an agricultural deity?
It is mentioned that she is a goddess whose temporary disappearance is written about in mythology, but I haven't found it (yet?).
Modern Worship
She would be a tricky one, but not impossible. With deities like this (little to no information), it just takes a lot of trial and error, as well as divination. We do know that she was invoked in rituals to aid childbirth so, she could be honored by new and expectant parents or anybody trying to conceive.
My advice would be to start with kind of generic offerings (ie water, bread). Do divination to ask her questions about herself. Intuition is a powerful tool as well, if you're shopping for groceries and see a vegetable and think "Anzili would like that" out of nowhere, then try it!
I will be on the lookout for more information about her, but here's her Wikipedia article.