Mine would actually come off fully. I looked up the company name on mine and rung and spoke them. They said they don't do covers any more and are actually going out making the couches as well as they are being imported straight in. They said people got annoyed trying to put them on as they were a tight fit.
I know in the past you could get replacement covers as I got one for my niece many years ago.
I did find http://www.littlebumchums.com.au/category/covers
but personally even though they look really nice $A45 is too much once you covert to NZ$ and would have to pay to get it here. I could buy a whole new couch on special.
Might get my sister to look in the likes of Target and Big W in Aussie as I found some old forums where people had got them found around 10-15.
I did consider sewing a cover but it would be really fiddly so maybe I might just make a loose on or give up altogether. The dog loves it as it is