Separate plates are needed for each color printed onto a full sheet of card stock.
Business cards can be printed -- using your computer and an inkjet or laser printer -- onto perforated business card stock available from your local office supply store.
Avery business card stock is often better since the edges are cleaner.
To present a cohesive color scheme, opt to use the same manufacturer such as Bazzill Basics or Prism for card stock and Reminisce for patterned paper.
You can purchase card stock paper in a variety of colors, and you don't even have to have a special program to create a beautiful card.