There is a somewhat sneaky way to get additional Liberty choices by assigning a LOW Loyalty Leader to a not very important colony to make into a Core World. Then every so often he will start disparging you to your other Governors, and you will be offered a choice of actions to take: if you let him continue to speak about you, you will lose 10 Control Points but gain a Liberty choice each time for your possible assignments of Culture Points. Then a number of turns later he will do it again, and again, and again, and again.
In my current game, I am letting this continue until I can choose the last 2 Liberty Ideology choices; no maintenance cost for Star Bases, and -25% to reduce decay rates for Cores. This will end up costing me 40 or 50 Control Points (I have enough Control Point income to be able to afford this) before I get rid of that Leader/Governor. I am almost there, he just needs to slander/disparge me one more time, and I can use Culture Points to get those 2 Ideologies (getting no maintenance costs on Star Bases should be very useful in the later stages of the game when we have a lot of Star Bases; and -25% to reduce decay will be useful as well). The lower cost Liberty Ideologies can also be accessed this way as well.
If you have some really HIGH Loyalty Governors you get from them occasional gains of 500 credits or 10 Control Points, which makes the loss of Control Points from the Low Loyalty Governor easier to handle.