Probable outcome with 9 deliverance engines?   You will turn some planets neutral, but not his whole empire.  As culture recedes, he'll recolonize.  Since he's an unfair AI, he has such a high resource cheat that this won't mean much to him.  If you're playing with Entrenchment (ie, he has starbases) then I don't think this will cause the game to end at all.

Best thing you can do to bring this to a conclusion is to make a massive swarm of bombers that turns everything in their path to dust.  Deliverance Engines give friendly units a damage bonus in planets under their effect.  Combine the Rapture's passive damage boost with maxed out beam damage upgrades and Advent bombers can incinerate a fully upgraded starbase in a few passes.

If you have enough time to build all of those up, it is possible to make him lose some of his worlds. I've found it best to assign them to hotkeys and stagger the firing and the targets; spread them around his empire and be constantly bombarding some part of his empire with your culture.

However, as Darvin has already pointed out, the best use of the Deliverance is to fire it ahead of your attacking fleet as you go after heavily defended planets - both depriving him of his culture combat bonus, and giving you the advantage of having yours as you assault fortifications.

On a similar topic I built the Vassari cannon and fired it before sending my force there.  Found that it did nothing.  Am I doing something wrong?

The Kostura has three effects.  The first is that it deals a small amount of damage to all enemy units, the second is that it stuns all enemy units for a short time, and thirdly it makes the target planet a phase stabilizer node temporarily... as in it's as if the planet has a friendly phase stabilizer there.

The Kostura damage is inconsequential unless you have 10 or so Kosturas, then it becomes gamebreaking since you can kill massive fleets very quickly (if the target planet is too far away, a smart player will run his fleet out of the system.  If it's close enough, though, the first Kostura will hit before he does this and stun him long enough for the others to arrive.  Very annoying, essentially a free win for the Vasari if they get this.

You can use its stun capacity in combat.  It doesn't affect friendly units, so just fire into battle and then get some free attacks off.  If you're really feeling nasty, you can deploy mines immediately after the Kostura hits.  The enemy will be stunned while the mines arm, and then they will be destroyed by the minefield you just created in the middle of their fleet.

Powerful as that may seem, the Kostura can do even MORE.  You can use it to turn enemy planets into phase stabilizer nodes.  This allows you to completely bypass front-line planets and jump directly to any planet you shoot with a Kostura.  If you want to directly attack their homeworld, you can do so.

So yeah, the Kostura is the most powerful superweapon by a massive margin.  The others just aren't even in the same class.

The Kostura is simply out of line with comparison to the other superweapons.  While one could argue that Novaliths (once you have a pair) are pretty deadly, I personally don't think so.  To get critical damage out of Novas, you need 4 or 5, by which point Kosturas are on the brink of being gamebreaking anyways. 

Personally, I think kostura stun needs to affect friendlies (otherwise you can just lay mines while everyone is stunned and watch them die before they can move away from the newly created minefield), and the damage needs to be either removed or changed so as not to stack to the point at which it's killing frigates.  Heck, just the phase stabilizer functionality alone makes it the most powerful superweapon IMO...

Is the phase stabalizer ability of the kosutara only in entranchment?

Only the Novalith's 40% (stackable) penalty to max population and the Kostura's temporary Phase Stabilizer Node are in Entrenchment.