There 's not much choice in Cairns. The Yacht Squadron has a travel-lift and small hard stand storage area. That would be your best bet if you were set on Cairns. The travel-lift can cross the road and park your boat on the hard by the Big Boat Shed. Some boats have long term storage there. The other option is Norship. They also manage the Yacht Squadron travel-lift. Norship does bigger boats including navy vessels, fishing fleet and reef tour boats and is more expensive as it is geared for large commercial boats.
I live in Port Douglas which is about a hour north from Cairns where I have 3 commercial boats as well as my Maramu.
John, Maramu #91 Popeye