You could probably use Shaker Chair tape from Shaker Workshops: http://www.shakerworkshops.com/catalog/shaker_chair_tape.php/tape

The risom line of chairs came about as a way of reuse of material. Specifically it originally used parachute material left over after WWII ( as I was told when I visited knoll). Therefore I'd try to look elsewhere then classic chair resources. I think seat belt material would look nice as well as a heavier lawn chair webbing -- both of which would come in multiple colors.

Google webbing. cheeptrims.com has some.

What purlgreyhound said. I've bought chair tape three times from Shaker Workshops, and it's really good quality.

Knoll will send them to you.

Thanks, all! The Shaker tape looks great, but I'm kind of concerned that the thinner width (1") will really change the design of the Risom lounge. b77, very interested in using Knoll straps. Any idea how much they charge for them? PS-Food for thought--I got inspired by this Sit and Read video in which they used Unis canvas for webbing: http://vimeo.com/16748760.

i've seen some done with recycled car seatbelt straps and they look really cool.

Knoll has a huge assortment of colors in the Risom strap material. Since they hold the license for the authentic chair you might want to start with them to keep your authenticity of the chair. If you know someone in the trade you can get 15% off your order, or wait for DWR to have their Knoll sale for a discount! Best of luck!