There seems to be no direct route via bus to get from Haputale to Deniyaya.
You will have to make your way to Ratnapura which is bus 99, then catch a connecting bus 62.
99 - Badulla - Colombo
Route passes through Bandarawela
, and Maharagama
62 - Ratnapura - Deniyaya
Route passes through Pemadulla, Madampe, Rakwana, Sooriyakanda and Buthkanda