Your only option is modding. In Civ5HandicapInfos (in BNW that would be in C:\Program Files (x86)\Steam\SteamApps\common\Sid Meier's Civilization V\Assets\DLC\Expansion2\Gameplay\XML\GameInfo) there's a value given for 'EarliestBarbarianReleaseTurn'. For most levels a zero is given, meaning barbs will appear from the start. I've never tested it, but if you would fill in a higher number, say 50, for the level you're playing at, you shouldn't have any barbs for the first 50 turns.
On settler difficulty they will never enter your territory.
They're simply absent from the level:
Code:
<EarliestBarbarianReleaseTurn>10000</EarliestBarbarianReleaseTurn>
Another option would be to do something with the amount of fog tiles needed to spawn a barb camp, figures for that are listed in Civ5Worlds, which is in the same place as Civ5HandicapInfos.
With changing that last setting I do have some experience, but then I set the amount of fog tiles lower, to raise the number of barb camps instead of lowering it. I like my barbs (uploaded once a mod here somewhere called 'More Barb Camps').
I do agree the games becomes easier with more barbs. If you increase the amount of barb camps a lot, it especially becomes very easy to snap up captured workers and gaining influence. It's like cheating.
What also would decrease their number, without modding, is having more CS's or civs on the available land. Increasing the sea level should also do the trick. Then there are less barbs because of less space, but there would also be less space for you.