There are some slower papers which can be used for contact printing. I've done this in the past without a darkroom, using 4x5 and 8x10 sheet film, though this could also be used for proof sheets for 35mm or 120.
The paper I've used in the past was Kodak Azo, which you can't buy new nowadays (it pops up for sale every now and then on some large format lists). It's a silver chloride paper, is slower than regular enlarging paper. I'm not sure if this is typical for all silver chloride papers.
For new paper, you can buy Lodima (http://www.michaelandpaula.com
), which was designed as an Azo replacement.
I have no experience with the Lodima, but I hear good things about it.
There's also Foma Fomalux FB 111 and Foma Fomalux 312 RC, which are supposedly "contact speed". I don't know how they compare to Azo or Lodima, as I haven't looked them up, but you can get them for cheaper.