For excellent book reference, cf.: F. E. Condon, “Study Projects in Physical Chemistry”, Academic Press, New York and London, 1963.          

Activity coefficients of what? Water?  Protons? Ions? Metal ions? This is rather complex area in physical chemistry. There is no quick answer. 

Dear Mr. Geletti, 

I would like to ask, specifically, the methods for calculating activity coefficient of individual metal ions in an aqueous solution.

For instance, activity coefficient of Fe3+ in a solution containing Fe-Cu-Ni-Co.

Kind regards, 

Maybe it would help if you can clarify why Debye-Huckel is not applicable. Because that would be the simplest way, actually.

First,  pKa (Fe3+) = 2. Therefore, "Fe3+" is probably hydrolyzed in your solutions and does not have a charge 3+.