Mr Durkan also gave a spirited defence of the restored power-sharing institutions and the pro-Belfast Agreement lobby inside and outside the Assembly.
He told delegates there was a compelling majority of people in favour of the accord in Northern Ireland and he described the power-sharing administration as "first class".
In a reference to the Reverend Ian Paisley's two Democratic Unionist ministers, the new deputy First Minister said he'd prefer it if Mr Peter Robinson and Mr Nigel Dodds would "come in from the cold".
"It is in the interest of their voters and believe me, they know that as much as I do but that is their decision.
"No matter, we will offer good government. It's what the people want and deserve.
"Especially as we enter a period of global economic uncertainty, people want their government to offer stability and they want their politics to guarantee peace."
Mr Durkan told party members that the SDLP were "not just dreamers and keepers of ideals" but also the masters of persuasion.
"It is what we do best. We in the SDLP have never had a hardware counter when we set out our political stall!
"Our only force is the force of argument. We have no Army - no guns, no bullets, no bombs, no plastic explosives and, we will ensure, no plastic bullets. By politics we stand."
He paid tribute to his predecessor and mentor Mr Hume and the former deputy leader and former Deputy First Minister Séamus Mallon.
He said they had both delivered ceasefires, dialogue and democratic agreement during their time at the helm of the party. "John the architect. Séamus the engineer," he described them. He stressed that the SDLP had pulled off these achievements with "not a bullet, not an ounce".
He continued: "We are the original not one bullet, not one ounce party.
"We now have vindication. We never sought victory. We have the vindication of seeing others work to our knowledge and of hearing them use our language after years of wasteful intransigence and wanton violence."
PA