We investigate the masses of cs (c) over bar(s) over bar tetraquark states in a diquark-antidiquark picture employing the relativized quark model proposed by Godfrey and Isgur. Only the antitriplet diquark states in color space are calculated. The diquark masses are obtained with the relativized potential first, and then the diquark and antidiquark are treated as the usual antiquark and quark, respectively, and the masses of the tetraquark states are obtained by solving the Schrodinger equation with the relativized potential between the diquark and antidiquark. The theoretical uncertainties induced by screening effects are also taken into account. It is found that the resonance of X(4140) can be regarded as the cs (c) over bar(s) over bar tetraquark ground states, and the X(4700) can be assigned as the 2S excited tetraquark state. When the internal excited diquarks are taken into account, the resonance of X(4500) can be explained as the tetraquark composed of one 2S scalar diquark and one scalar antidiquark. In our approach, the X(4274) cannot be explained as a tetraquark state; however, it can be a good candidate of the conventional chi c1(3(3)P(1)) state. In addition, other charmoniumlike states chi(c0)(3915), X(4350), X(4630), and X(4660), as the cs (c) over bar(s) over bar tetraquark states, are also discussed.