I'm guessing tilemaps are not rendered when they are outside of the viewport, so it will not be possible to paste them on canvas/paster object. There are two solutions -
1. Temporarily move tilemaps for player 2 to the viewport, paste them, and move back to their original position. This can all be done in one tick. Don't know if this can cause problems with player #1, maybe you'll also need to temporarily disable collisions.
2. Keep the tilemaps for player 2 on the screen, but make them invisible, or put them on an invisible layer. Seems like invisible tilemap can be pasted on Paster.