Butterworth filter with non arbitrary component
The quickest method is plug the circuit into a simulator like LTSpice to find values for the unknown components that produce what you feel to be the best response. Sims like this are free but have a steep learning curve but with something as simple as this is probably worth the effort and you'll never look back once you have got the hang of it because you'll be able to use the sim for all manner of electronic circuits.

Algebraically, this could be an awkward problem to solve but numerically it'll be a breeze to a sim.