If one of the cysteine residues is within a ligand binding site, you can block its reaction by including a saturating concentration of the ligand. After labeling the other site and removing the excess labeling reagent, you can remove the ligand and label the previously blocked site.

If that method is not an option, then you have no way to prevent both sites from labeling simultaneously, although they may label at different rates. You would have to use a different strategy, such as by making an expression construct designed to be labeled by a specific reagent, such as the tetracysteine/FlASH system, or by making a fusion with a fluorescent protein, or by using a fluorescent antibody specific to an epitope added to the protein (such as FLAG).

Dear Dr. Adam B Shapiro! Thanks for the reply. I would preferably first check with the construct for specific reagent treatment. I will let you know how it went. Thanks again :)

Not sure if this will work for you: There might be a way to protect the N-terminal Cys, so you could attach the C-terminal label first:Article Fast and Stable N‐Terminal Cysteine Modification via Thiazol...

Thank you, Dr. Wolfgang Schechinger. It was helpful indeed.

Thanks all for your suggestions. I was able to use peptide tags for specific conjugation of the 2nd dye conjugate to the protein. Luckily, no native cysteines in my protein so I introduced them for conjugation. Thanks again!@Adam B Shapiro & Wolfgang Schechinger