Generation of coherent terahertz (THz) radiations by nonlinear interaction of a pair of coaxial q-Gaussian laser beams with underdense plasma has been investigated theoretically. Owing to the relativistic increase in electron mass under the intense fields of the laser beam, the resulting optical nonlinearity of plasma leads to cross focusing of the laser beams. Because of the nonlinear interaction between the two laser beams, the oscillations of plasma electrons also contain a frequency component at beat frequency and thus generate a nonlinear current density at frequency equal to the difference of the frequencies of the incident laser beams. This nonlinear current density acts as a source for coherent THz radiations. Starting from the nonlinear Schrodinger wave equation a set of coupled differential equations governing the evolution of beam widths of the laser beams and intensity of generated THz radiations with longitudinal distance has been obtained with the help of variational theory. The equations obtained in this way have been solved numerically to envision the effect of laser as well as plasma parameters on the intensity of generated THz radiations.