Sorry, but I don't think this is possible. It is possible to increase maximum allegiance through research, but that applies to all planets in your empire. Also, Sins has no random events such as rebellions, it is a straight RTS in that regard. And I don't think its possible for the loss of a planet to cause other planets to lose allegiance.
If you want a game with a system where you have to keep your people happy and can do things to boost their happiness, and the loss of a colony will negatively affect the morale of your citizens, play Sword of the Stars: A Murder of Crows. It has a wonderful morale mechanic, once you get used to how frakking hard it can be to keep people happy especially once your civilians hit their population limits.
EDIT: You can grab the Sword of the Stars Ultimate Collection on Impulse for $29.99. Totally worth it, althouh I would grab Argos Naval Yards ($8.99, less than Entrenchment or Diplomacy) as well so you can have access to the latest patches.