X-ray diffuse intensity measurements have been performed at room temperature on the local arrangements of intercalated Cu atoms in the layered compounds Cu_xTiS₂ with compositions of x = 0.13, 0.23, 0.32 and 0.37. Two types of diffuse maximum due to the different in-plane correlations of Cu atoms appeared, depending on the composition. For the lowest content of Cu atoms (x = 0.13), diffuse maxima appeared at 1/2,0,1/2, 0,1/2,1/2, 1/2,1/2,1/2 and their equivalent positions. For the highest content of Cu atoms (x = 0.37), diffuse maxima appeared at 1/3,1/3,1/2, 2/3,2/3,1/2 and their equivalent positions. In the cases of x = 0.23 and 0.32, the two types of diffuse scattering coexist, with intensities depending on the composition. From the experimental results, we expect the following in-plane ordered structures for the low- temperature phases in the compounds Cu_xTiS₂:2 × 2 and ((3)^1/2 × (3)^1/2)R30° structures in Wood notation, whose stoichiometric compositions x correspond to 1/4 and 1/3, respectively. The diffuse rods are modulated along the scan parallel to the [001]^* direction centred on 1/2,1/2,0 for x = 0.13, 0.23 and 0.32 and on 1/3,1/3,0 for x = 0.23, 0.32 and 0.37, with maxima appearing at every half-integer. This reveals an enhancement of the three-dimensional nature and a stacking sequence ... is deduced. Finally, the observed in-plane diffuse intensities are compared with the calculated ones, using a linearized mean-field approximation for the correlations of a binary Ising system well above T_c developed by Clapp and Moss.