As per my knowledge, titration method is simple technique: Dissolving of nano material in acid or base and addition of indicator followed by titration against base or acid till color change. If you have any suggestions, please let me know.
Have you considered performing a Temperature Programmed Desorption (TPD) analysis? Basically it involves adsorbing a probe gas on your sample, followed by programmed heating to desorb the gas molecules strong adhered to the nanomaterial surface, and analysing the desorbed molecules coming off the surface. With a known amount of nanomaterial, you will be able to calculate the concentration of the acid/base sites (mol/g).
Generally, you perform this either in a vacuum system, or a flow system (inert). Usually an MS detector is used, though this is by choice, as long as you have a detector capable of detecting the probe gases.
Simplistically, use NH3 as the probe gas for acid sites, and CO2 for base sites.
This analysis is extremely useful and versatile since you can use a variety of different probe gases of your choosing (depending on what you want to analyse), while also being able to calculate heats of adsorption based on the results, but it is also a very extensive system. I would advise on reading up on this if this does indeed interest you.
One additional technique you can consider, is using a Hammett Indicator. Essentially you adsorb an indicator of choice on the surface of your sample. You can evaluate the concentration and strength of the sites, providing you have chosen your indicator wisely. Have a read through this attachment shown.