The sheet music can be seen at Indiana University:


A STARRY NIGHT FOR A RAMBLE
Samuel Bagnall
In "Popular Songs Sung by Harry Vandemark, the Great Comic Vocalist"
New York: E. H. Harding, [18--]*

[The lyrics are exactly the same as those posted by Bob Bolton above, which he says came from a broadside. They begin:]

1. I like a game at croquet or bowling on the green,....

[* I found it mentioned in a couple periodicals in 1872. The sheet music was also published in Peterson's magazine, Volumes 63-64 (Philadelphia: [C.J. Peterson], Oct. 1873), page 238. However, that version has only 3 verses. The source cited there is "As published by Sep. Winner & Son,...Philadelphia."]