Becoming too big in Civ 4 is costly. If you overextend yourself during colonization or war, there is no easy way to save yourself. The Pedia suggests that you should withdraw defenses and hope for barbarians to come.

A player should have the possibility to allow a city's secession by pressing a button. That would hand over the city to the Barbarian civ. The player would receive some gold as compensation (from selling charters and property to the local ruling class). This would only be allowed during peacetime, to prevent secession of cities about to be lost.

Could this possibly be done through the events manager?

Becoming too big in Civ 4 is costly. If you overextend yourself during colonization or war, there is no easy way to save yourself. The Pedia suggests that you should withdraw defenses and hope for barbarians to come.

A player should have the possibility to allow a city's secession by pressing a button. That would hand over the city to the Barbarian civ. The player would receive some gold as compensation (from selling charters and property to the local ruling class). This would only be allowed during peacetime, to prevent secession of cities about to be lost.

Could this possibly be done through the events manager?

It could be done, not easy, but definitly doable. You would want to make sure you don't allow players to exploit and make easy money by selling cities, taking them back with force and then repeating.

I think it would be better if there were no compensation

Make compensation dependant on the value of the city. Secession of a worthless size one city shouldn't yield a thing (maybe even cost a little to organize an administration), while secession of a powerful, culture-rich or productive city should give you quite a lot of gold.
But since conquest of cities involves some turns of revolt and destruction of improvements, it's not very likely that people will give a valuable city away just for quick money and recapture. Good idea?