This was a project I'd tried a couple of years ago that wasn't working like I wanted at the time, so it's been on the unfinished 'to do' list too long. This time I ended up with a much better working model. The paracord is zigzag spooled(like you may find with cordage you buy from store that comes on a spool) onto the PVC pipe over the carabiner. With the carabiner held in hand or secured to gear, the cord can be pulled off and quickly deployed from the free spinning spool. If the ends of the spool were flared/capped, keeping the cord from spilling off the spool, it would be easier to coil cord onto the spool...
The biner I used is an Omega Locking D Carabiner that I've had for almost 20 years, that has a tubular formed body compared to some that have odd shaped cross sections. The oval and D shaped carabiners will have the most room for carrying more paracord, so that's what I used. The diameter of the carabiner tubing was slightly smaller than the interior spool diameter, that I intended to put over it, which is just what you need to measure for.
I had some leftover 1/2" diameter PVC pipe, to use for the spool, stored in the garage from a light tent project several years ago. I used a hacksaw to cut a 3" long length to fit the carabiner. Of course you can't just slide the PVC onto the carabiner, so I cut it again down the center of the length of the pipe, making two halves.
I fit the two parts around the carabiner and used gaffer/duct tape to wrap around them and secure them back together. The pipe then spins freely around the carabiner. I wrapped as much paracord on the spool as I could, which was about 40 feet worth, and still be able to open the carabiner gate just enough to slip it over nylon webbing/PALS/MOLLE attachment points on a bag, backpack, strap, or vest.
The PVC pipe makes for a firm spool where my previous tries with softer rubber and plastic tubing would give/warp too much when adding the paracord, creating too much friction and the spool wouldn't freely spin around the carabiner. I may eventually add a short tutorial for making this project later.
A similar product, that might could be used/converted to dispense paracord, is a cave reel /diver's spool. They come loaded with string, but it may be possible to put some paracord on them instead, although I don't know how much would fit...
Earlier in the year, a friend made me some smaller bead sized metal tubular spools with flared ends. I'd tried finding similar and making my own but was unsuccessful. My intended purpose was to add thread, fishing line, or some 0.9mm braided nylon line onto the smaller bead spools and them add them to a survival type paracord lanyard. My photo shows the beads next to a penny for scale, and the paracord lanyard is a 'Bug Belly Bar' tied by Manny, who also made the beads.