Are your wheels solid or do they have spokes?  If they have spokes (even wooden ones), a couple of U-shaped bicycle locks (or something similar) would probably be the cheapest way to do it. You could screw a large-holed eye-screw into the side of your cart near each of two wheels and run the bicycle locks each thru the eye-screw hole and then around one of the spokes or around the “tread” of the wheel between two of the spokes.