In the paper we introduce a new approach to obtain nonlinear generalized coherent states, which involves creation / annihilation operators that come directly from the expression of energy eigenvalues of the examined quantum system. Unlike "classically used approaches", in our one it is not necessary to know the generators of the quantum group corresponding to the considered system. Using a new technique of normal ordering of arbitrary creation / annihilation operators (DOOT), both well-known and also some new results, which do not appear in the specialized literature, are obtained for the generalized nonlinear coherent states.