Paul, you can use the Parameter Bounds pulldown in the Nonlinear platform, specify the bounds you wish, and then iteratively fit a linear model.
The Nonlinear platform will make you specify a model in the Formula Editor and supply some Initial Values for the parameters. You won't enjoy some of the model diagnostics you might be using in another platform (R^2, for instance, is not provided for nonlinear models), but at least you can constrain the parameters appropriately and (if your model converges) get a hopefully useful answer.