Thanks to NYGPS Members Rich Rodgers (audio) and Jessica M. (video attachment) here is the NY Giants March written by Horace Stoneham and played at the Polo Grounds. Many members and people have been mentioning this song for decades without finding it. Here it is! Enjoy!! (Click on youtube link on bottom.
We’re calling all fans,
All you Giants ball fans.
Come watch the home team,
Going places ‘round the bases.
Cheer for your favorites,
Out at Coogan’s Bluff.
You’ll see those Polo Grounders,
Do their stuff!
(words by Horace Stoneham)