Probably a more lengthily description of the system you want to study would help in giving you a more detailed answer. There are several protocols available to specifically label molecules that contain amine groups. Which one to use depends on the specifics of your model system.
As to how to determine the exact number of amine molecules, this can be attempted via fluorescence assays, however, it is not necessarily trivial. I can see two options, one is the generation of careful calibration curves by measuring surfaces of known density of amine groups on the surface, and then comparing the measurements of your model system with that calibration curve. Much in line with beer-lambert law methodologies. The second option is to actually calibrate for the intensity that you would observe per fluorescent molecule (in your given experimental conditions). This is dependent on several aspect like, absorption cross section and quantum-yield of the label, excitation wavelength and power, collection efficiency of the microscope and so on. In these two articles some colleagues and I describe some of the theory behind brightness measurements in fluorescence, maybe you can have a look in there (and references therein) for inspiration:
Lin, H., Camacho, R., Tian, Y., Kaiser, T. E., Würthner, F., & Scheblykin, I. G. (2010). Nano Letters, 10(2), 620–6. https://doi.org/10.1021/nl9036559
Thomsson, D., Camacho, R., Tian, Y., Yadav, D., Sforazzini, G., Anderson, H. L., & Scheblykin, I. G. (2013). Small, 9(15), 2619–27. https://doi.org/10.1002/smll.201203272
Thank a lot for your answer. I have a polymer surface on which graphene is coated. Above the graphene layer amine groups are present. I also came to know quenching occurs in graphene oxide. What kind of surfacatant should I use to reduce quenching?
You could use the commercially available reactive fluorescent dyes which are routinely being used for attaching fluorophores to proteins (extrinsic fluorophores). These dyes react specifically with -NH2 or -SH or -COOH groups present on the amino acid side chains. From their fluorescence, you could quantitate the number of free NH2 groups. I hope the -NH2 groups are free.
There could be some complications due to quenching, dimer formation and excimer formation. Choice of the dye is going to be critical to avoid these complications.