A consultation prompted 620 responses, with 98% saying owners should clean up after pets and 69% saying dogs should be excluded from play areas.
But 70% did not want to see dogs excluded from beaches.
The council's environmental and public protection scrutiny committee will consider proposals on Monday.
Plans that could see owners compelled to put their dogs on a lead and a ban on the animals in playgrounds will be discussed by Carmarthenshire council.