Depends on what you mean by "watermark". If you mean "faint superimposed image mixed into what's displayed/printed", Sean's answer is correct. If you mean traditional watermark (image embossed into a piece of paper by controlling its translucency), Lemonie's answer is correct.
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Yes, you can design a faux watermark using colors instead of B&W. Use MS Office or many other word processing packages to do it. (Can also be done using photo editting programs like Photoshop, Paint.net and others, although the process is a little more complex.
Watermarks aren't coloured, you are thinking of something else. You might be able to make your own papers with coloured-inserts, how much experience do you have with paper-making? L