Specifically, it might have been the first word the original creators found to fit the positive, uplifting message you would expect to find in a... in whatever Spring Yard is. And it is is a fun word. Cope! :-)
Paradox. They're telling you to cope with the fact that the signs say "COPE", so that means that they're telling you to cope with the fact that they're telling you to cope with the fact that...
If I really had to come up with a reason, I would call it a strange half-hearted effort by Robotnik to lessen resistance. That's right, he's taking over and turning all of your friends into cold, unfeeling robot badniks, so... deal.
From the Development Gag page: "The first game also has glowing letters reading "COPE" in the Spring Yard Zone, which is the acronym for one of the graphics processing routines used by the developers."
This troper has always interpreted it as encouragement or possibly a snide remark concerning the player's impending and inevitable troubles in navigating around Spring Yard's formations of bumpers.
This troper heard that there was once a company that made parts for pinball machines by that name. It might be a joking Shout-Out to them due to the theme of the level.