Okay had a look at my 5 American songsters and not much in the way of Child Ballads pops up. My undated 'Forget-me-not Songster' seems quite seminal, and Jonathan might be able to date it.
It has
Captain Ward
Captain Glen
The Mermaid
Barbara Allen 'It fell about the Martinmas Day'
Lord Thomas and Fair Eleanor 21v (of interest to Richie)

The 1839 N C Nafis, NY 'The American Songster' has
Barbara Allen 'In Scarlet Town where I was born
and the same songster printed in 1851 by Cornish and Lamport NY has the same version.

I have another similar songster without title page that has another copy of the Mermaid which can be dated to 1846.

Steve Roud has more of these than I do and I suspect some of the collectors on Ballad List will have many more.

I've just pulled an interesting volume off the shelves which I'd forgotten about. American Song Sheets 1850-1870 by Edwin Wolf 2nd. It seems to be mainly sheets by De Marsan and is only a catalogue, but I haven't yet included it in my own indexes so it will be worth looking through for interesting ballads, though I think I've got copies of most of De Marsan's output.