Dried tumbleweed is a brown. You can also use shredded paper, Paper towels and the cardboard tubes inside paper towels and toilet paper rolls. We shred all our junk mail and computer paper to add to our compost.We throw all our used paper towels in our compost bucket. Hope this helps.

Along with the items that greenguy composts, I also tear up all our used newspapers and cardboard boxes and compost them as "browns." Apparently, the colored inks used in newsprint and cardboard boxes are considered OK now that soy-based inks are used. The glossy colored paper catalogs, magazines, etc., I don't use in my pile.

Here's where I found the quote below:
http://www.grist.org/article/umbra-papercompost/

"Pigments themselves still contain heavy metals such as zinc and copper, although overall amounts of heavy metals have been reduced. Although toxins are present in quite small amounts, all the sources I consulted agreed that contemporary printed newsprint, including colored newsprint, and cardboard boxes are safe for garden use. Glossy inserts, shiny ink of any sort, magazines, and colored paper do not make appropriate compost or mulch materials, due to a higher prevalence of toxics within the paper and ink, and likelihood of "de-inking" (ink sliding off the paper into your garden)."

I would think that tumbleweed would work great, as a "brown" addition to your compost pile, provided that you are able to somehow break it up into smaller pieces. I am able to shred the leaves from our maple tree with a mulching lawnmower, but I don't see how this could be done with tumbleweed. The plant can be ripped apart by hand, I guess...