He died at the weekend after a long illness, aged 77.
Mr Laing was a fixture at Moana Pool for 40 years, and it was often said that he must have taught half of Dunedin how to swim.
His greatest coaching success, Olympic gold medallist Danyon Loader, told mourners on Wednesday that the coach gave him the courage to try what seemed impossible, and always maintained a sense of humour.
New Zealand swimming coach Jan Cameron spoke of her friendship with Mr Laing, telling mourners that he never changed in the 40 years she knew him.
Ms Cameron said he was loyal, passionate, funny and knowledgeable, and had an unwavering commitment to helping people become the best athletes they could be.
Mr Laing and his wife Betty also ran Dunedin's Moana House, a rehabilitation centre for troubled young men.