If you really want to get right down to it, adults love to color as much are their kids do. If you dont believe us, think about all of the artists that do oil and watercolor paintings, those that do pen and ink drawings and watercolor pencil drawings and artwork. This is simply the more appropriate and acceptable way for adults to continue coloring as we all did as kids. This is partially why both adults and children alike really enjoy having SpongeBob printable coloring pages available to them to color on.
You can metaphorically take a page out of a coloring book, and break up the work into a few sections. Each team member or group within the team should first be instructed on which part of the page they are going to color, let them know what color they can use, and when their turn will come up. Next, after each team member has finished their part of the coloring than take the completed picture and hangs it up so that every one can see their part of the picture and the entire teams contribution.