Capability on a one-sided specification (where it is possible to go outside of that limit) is very difficult to accomplish. As you know, Cpk is derived (in part) from Cp, and if you do not have an upper and lower limit, you can't calculate Cp. Introducing an artificial limit doesn't help, as it can influence the results without really being meaningful. I do not know of a statistical model which can take something like that into account and still calculate Cp and Cpk accurately.

Have you tried plotting your suppliers measurements as a run chart, with precontrol limits (based on historical data from them) to demonstrate that their process is within control? That may be the easier way to do this.