1. XPS is a useful method to determine the functional groups on the nanoparticles surface
2. Try the simple Schiff base reaction of your amine groups with salicylic aldehyde - it`s very sensitive :) With UV-Vis detection.
3. There is a commercially available dye called fluorescamine, which is suitable to quantify surface amine groups. It binds to amines and becomes fluorescent. For your specific application you will need to calibrate.