First off let me say this class was not what I expected at all. I went in expecting some flashy new features that mimic the other class', and was pleasantly surprised to find myself wrong. The Godling is a strong, balanced class that brings something new to the table. With all the different Domains, divine traits, bonus feats, and scion talents to choose from, you are pretty much guaranteed to never see two Godlings exactly the same.
The Lineage Domains are nice, but I think certain Domains may get selected more often than others, especially since you need a Scion Talent to cast spells from Domains. Destruction and the Elemental Domains come to mind, as well as the Weather Domain. But that just might be my way of thinking.
When it comes to Divine Traits, I have to say that I like Seaborn and Trophy Taker the most. All of them are well written(though it did take me a few moments to understand how Trophy Taker worked). I think you got most of the traits/abilities the demigods Greek myth had when you went with this route.
Scion Traits are interesting, and help keep the “half-mortal” aspect of the Godling evident. The Greater Scion Traits balance the “half-mortal” aspect with the “half-divine” parentage. Good abilities in both features.
The Demigod capstone is very interesting. It's not like any of the other capstone abilities, so it's unique in what it gives you. Giving any character a cult to look forward to is going to be hard to handle, but limiting them by level using the Leadership feat guidelines is a great idea. The spell-like abilities and becoming harder to kill are icing on the cake. A neat capstone well worth the wait.