I have been working on Newborn diaper covers using the Turn and Topstich method I've been using with my son's covers. They have double gussets to hold in all that Breast milk poop, and has a dip on the belly panel to avoid rubbing against the umbilical cord while it is still attached.
Admittedly this diaper cover was MUCH more difficult to sew because it's so tiny. This diaper cover doesn't lay flat. It "concaves" to better fit around baby's legs and bum. It doesn't drape over my sewing machine like most projects. It curls around my sewing foot as I am trying to sew the tiny diaper pieces together.
But I am VERY happy with how these came out. I plan on making Small sized and One Sized diaper covers so that I have a stash that can take her all the way to potty training. I don't think I will be getting much sewing done while I have 2 under 2.
Tutorial on how I did the leg gussets can be found here.