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Barbarian horde grows 0.01 per month so they will spawn, eventually. If there is a neighbor province with a higher barbarian horde and with lower civilization rate, you could place your militia there and hope they spawn quicker. They might then pass through this province you wish to colonize and make a bigger horde. I realize this is probably a silly suggestion but I can't see any other way to make them spawn quicker.
 
Barbarian horde grows 0.01 per month so they will spawn, eventually. If there is a neighbor province with a higher barbarian horde and with lower civilization rate, you could place your militia there and hope they spawn quicker. They might then pass through this province you wish to colonize and make a bigger horde. I realize this is probably a silly suggestion but I can't see any other way to make them spawn quicker.
In fact you DO NOT want barbarians to make a snowball effect. Never ever. And that's because of this bug: http://forum.paradoxplaza.com/forum/showthread.php?582054
 
I am starting to feel a little silly leaving a militia in an uncolonised province in the hopes that the barbarians will come out of their holes.

Walk them around to the neighbour provinces and back with shift+click (to create the path so you don't have to click again every once in a while) because it seems that Barbies rather attack moving units than standing ones. That's the only effective way I know.
 
In fact you DO NOT want barbarians to make a snowball effect. Never ever. And that's because of this bug: http://forum.paradoxplaza.com/forum/showthread.php?582054
This is also true. You only get the slaves from the original horde, not the total horde army.

There are times when allowing them to snowball isn't so bad, though. Specifically, when they decide to march towards an enemy's lands instead of yours ;)

Walk them around to the neighbour provinces and back with shift+click (to create the path so you don't have to click again every once in a while) because it seems that Barbies rather attack moving units than standing ones. That's the only effective way I know.
Yeah, I've noticed this as well. They do seem to prefer moving units.
 
Walk them around to the neighbour provinces and back with shift+click (to create the path so you don't have to click again every once in a while) because it seems that Barbies rather attack moving units than standing ones. That's the only effective way I know.

If I have several armies near the border I usually organize them to move through the barbarian provinces in a manner that soon after the first army has left the barbarian province second one arrives. In that manner there is almost always moving army in the province which I desire to colonize.