So I recently got to work designing and building my own Nerf gun. I drew some crappy diagrams in Paint to show you before I attempt to explain how it will work.
Gun ready to fire:

Trigger pulled, gun firing:

Next round entering chamber, trigger still held down:

Next round advancing. Trigger released:

Round completely advanced, ready to fire again:

The semi-auto effect will be acheived using a spring-return pneumatic cylinder working in conjunction with a QEV. The cylinder serves as the air chamber for the gun. When air is supplied, it enters the cylinder and causes it to extend. The cylinder is connected to a "bolt" which moves forward to seal off the breech while advancing the next round.
When the QEV is piloted, the air inside the cylinder moves out through the barrel and fires the dart. The spring built into the cylinder causes it to retract. Since it is connected to the bolt, the bolt slides back and exposes the breech allowing a new round to enter the chamber.
The problem with my design is that the bolt starts moving back the instant the dart is fired. If air is still moving through the barrel while the breech is exposed, I may lose some pressure to the magazine. I will try to compensate for that by making the bolt and it's travel longer than the breech opening. Hopefully the breech isn't exposed until the dart has completely left the barrel.
The QEV will be controlled by a 3-way, normally open, toggle control valve. (It functions similar to a slide-check. Air is moving through until the valve is closed. Any air in the output side of the system is exhausted.) Unfortunately it's proving incredibly difficult to get a hold of one of these. I found down a company that can make one for me but it will take a while.
So far I've got all the parts except that valve. I bought an 1/8" QEV off eBay and the seller generously sent me 3! The air cylinder works great and cycles very fast with the QEV. The difficult part when I go to build it will be cutting a neat breech as well as a slot to connect the bolt to the cylinder arm through the 1/2" sch80 barrel. A 1/2" router bit fits well into the PVC so I may use a router. If that doesn't work I'll have to do it by hand with a Dremel.
I will have to make my own darts for this gun because I expect to burn through darts pretty fast and NERF brand darts are expensive. For that I will use 1/2" foam backing rod. The darts cannot have suction cups either, they must have a uniform diameter. I will most likely embed an airsoft bb into the nose of each.
Edit: Here is a video of the cylinder connected directly to a slide check (didn't have the QEV at the time, but it's the same idea)
http://s237.photobucket.com/albums/ff15 ... IM0755.flv
(someone mention to me that this video suggest something inappropriate... haha...)