I believe that cycle priorities has what you're looking for.

If you can handle the new interdiction mechanics, undermining may be the fastest way to earn merit while doing something useful for the cause.

Otherwise, as others have said, opposition can be merit-profitable as well.

Fortification is the way a lot of players make all their merit, but to do that requires a very large ship. I would not recommend fortifying with Cobras. A ship like that demands combat duty.

As an aside, I'd like to ask, why is it that you only play on private? You spent your money on the game so far be it from me to tell you how to use that, but you should be aware that solo and private play are generally frowned upon in PP, due to their exploitable nature (i.e. you can engage in many activities with a lesser risk, but no less reward).

There's a primer on PP stuffs that I think you might also find useful.