In this work, we calculate Flory-Huggins phase diagrams for correlated random copolymers. We achieve it in two steps. At first, we derive a distribution function of two-letter A, B copolymer chains depending on the fraction of A-segments and ABduplets. Then, we use the method of moments, which was developed by Sollich and Cates [Phys. Rev. Lett. 80, 1998, 1365-1368] for polydisperse systems, to reduce the number of degrees of freedom of the computational problem and calculate phase diagrams. We explore how the location of transition points and composition of coexisting phases depends on the fractions of A-segments and AB-duplets in a sequence and the degree of polymerization. The proposed approach allows taking into account fractionation, which was shown to affect the appearance of the phase diagrams of statistical copolymers.