You'll have to determine what material the binder is covered in. Vinyl?
Check with Nazdar, as they have a comprehensive line of inks for various substrates. Other than getting the right ink, you'll probably want to print through a 230 or higher mesh count, depending on the viscosity of the ink you end up with. I print yard signs with a 230. On the other hand, I printed some royal blue nylon backpacks with white plastisol with nylobond additive, and I got the best print with the 305 mesh.