Constrained Linear Regression in Python

You mention you would find Lasso Regression or Ridge Regression acceptable. These and many other constrained linear models are available in the scikit-learn package. Check out the section on generalized linear models.

Usually constraining the coefficients involves some kind of regularization parameter (C or alpha)---some of the models (the ones ending in CV) can use cross validation to automatically set these parameters. You can also further constrain models to use only positive coefficents---for example, there is an option for this on the Lasso model.

Recent scipy versions include a solver:

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.lsq_linear.html#scipy.optimize.lsq_linear

scipy-optimize-leastsq-with-bound-constraints on SO gives leastsq_bounds, which is scipy leastsq + bound constraints such as 0 <= x_i <= 255.
(Scipy leastsq wraps MINPACK, one of several implementations of the widely-used Levenberg–Marquardt algorithm a.k.a. damped least-squares.
There are various ways of implementing bounds; leastsq_bounds is I think the simplest.)