After measuring the zeta potential of my positive nanoparticles I attain a negative zeta potential. I also attain a negative zeta potential for negatively charged particles. The nanoparticles are polystyrene with either NH2 or COOH groups attached.
You may want to have a look at the buffer you are using to measure the zp, specially the pH. If it is basic, NH2 groups are not ionized and therefore you would not detect positive charges.