History of "My Pigeon House" song, German?

I am researching a children's song called "My Pigeon House." The words vary, but this is the general idea:

My pigeon house I open wide

And I set all my pigeons free

They fly away o'er every stoop

And they perch in the highest tree

And when they return from their merry, merry flight

They fold their wings and they say, "Goodnight"

Coo, coo. coo, coo, coo, coo, coo, coo

Coo, coo, coo, coo, coo, coo.

The tune resembles the German (Swabian) folk song "Muss Ich Denn"

At what point did the "Pigeon House" words come into being? Was it in Germany? Did it then spread in the German language through Europe before coming to the US, where it was translated into English.

Or were the "Pigeon House" words first written in English, or possibly Spanish?

I am especially curious whether it was passed down through Mennonite/Amish/Pennsylvania Dutch groups. (Yes, I know they generally wouldn't sing a non-religious song.) But I have seen numerous posts saying the song was passed down to them by a German ancestor who lived in Prussia, and others who have Pennsylvania Dutch background. All these groups were associated with northern Germany way back, but since only the Mennonites were in Prussia it can't have been from there.

As an added twist, I found a German version of "My Pigeon House", but the tune is different!!