Size your paper with soy milk, let it dry/cure 12-24hours. Then apply some pomegranate extract, or any natural dye extract, natural earth pigment, etc., to the surface of your paper. Allow to dry. Btw you CAN do this for paper pulp as well but this becomes a little trickier and is a bit on the advanced papermaking side of the spectrum.
You need to allow your paper to cure for 3-6 months, depending on the heat and humidity levels of your locale, BEFORE you rinse the excess dye off the surface of the paper. Not exactly a quick project I know BUT the colors can be quite stunning. I highly suggest working with papers of mixed fiber content, not just cotton rag. Experiment with flax, hemp, silk, recycled sari, papers for your natural dye projects.