I'm sure most temples are great to stay in at Koya-san. I stayed at Shojoshin-in this past spring and thoroughly enjoyed myself.It was somewhere around 11100 yen (for myself, alone) and had nice accommodation: http://www.flickr.com/photos/mchao/3397487279/in/set-72...
Plus, it's located right near oku no in cemetery, which I wandered at night to great spooky fun. And the two meals I had were great--amazing homemade tofu.
You can book the place on www.japaneseguesthouses.com. The site also has several other temples to browse through, which may fit your criteria better.
Happy hunting.