Meadowind, I travelled a few miles on a hog last trip & I gotta say that I can't recall seeing a trike either, like Simon stated.
I will gladly point you in the right direction & you can give these guys a go...........If there is a trike hire place, Sumon the boss will know all about it.
I recommend these guys to all, if you're ever needing a Harley or similar to rent.
Their website is
:: นิตยสาร ไรด์ ไทยแลนด์ แมกกาซีน - Ride Thailand Magazine
By the way..........Helmets are required on trikes here in NSW....would imagine same for rest of Oz too.
All the best with your travels.