In this paper we extend our previous study of decaying turbulence in two dimensions by simulating driven turbulence within a no-slip square boundary. Unlike other studies of driven turbulence we drive the turbulence by means of a cylindrical stirrer on a trajectory that is a Lissajous figure with a 2:1 frequency ratio. The turbulence is generated by the vortices that are produced behind the cylinder as it moves through the fluid. As expected the length scale of the vortices grows but the scale is limited by the side length of the square boundary, and the fact that the cylinder cuts through any large vortex. We show that the spectrum and correlation functions agree closely with theory and with other simulations. Interesting questions that arise from the study are (a) would the results be similar for other Lissajous figures, and (b) what are the minimal properties of any stirring trajectory that will produce turbulence with properties that are close to those of isotropic homogeneous turbulence?