Citation please? Offhand, I can think of nothing that would prohibit carry there...
this obviously isn't hardcore verification, but perhaps will jog memories
Gun carry was prohibited in Indianapolis city parks until the state voided such local ordinances. The Monon (within Indianapolis) is a city park. I'm not sure what its status is in Carmel or what the laws were there.
Guns To Be Allowed In Playgrounds - TheIndyChannel.com