Claude Okin, who oversees a tennis club empire on Long Island and beyond, said during a recent conversation at the Sportime club in Amagansett that when his wife, Hana Sromova, a former longtime pro tennis tour player, and Sue De Lara first suggested he add pickleball — a paddle game confined to a court one-quarter the size of the one used for tennis — as an offering at the nearby Sportime Arena he leases, he was dubious.