The New York Historical society has a copy in the Luce Collection, but I can't read it online at all. But if you're in the city ...

I too would like to see whether my NY Loyalist ancestors (Harpel or Harpell) signed the petition. Because there were so many signatories it could be. By the way, I believe that this petition had so many signatories not because it was more popular than the Declaration of Independence, but because it was available at a tavern for any to sign over the course of several weeks. There was no such opportunity for patriots to sign the D of I.