Alex,
Another line of enquiry might be to check out the list of Camera Clubs on the FCC (Federation of Camera Clubs) of NSW website and then send a message to the clubs individually asking if they'd circulate your request to their membership, asking if any members have a darkroom you could use. Don't be put off by the club locations - there are members of my club who belong to two or even three photographic clubs around Sydney and they're often miles apart. Having said that, most have gone digital but but there are still a few members in most clubs who have a darkroom - used or not.