Some help please

[Warlord Adamus]

"What do you do if it's the only colonized planet in the system? Is there absolutely no other way to stop the riots? "

Move a fleet over the planet you want to stop rioting (10 ships is a good number). The very next turn the log message will say happiness has improved. In 3 to 4 turns the orbited planet will turn from rioting to angry, allowing you to quickly build a pacification center.

[Instar]

It depends on which facility you have, the System wide one, or the Planetary one.