Step 1: Make the Bottom
I'm not going to get too specific with measurements here, since my goal was to make a one size fits all dispenser. I just took all the rolls of tape I had lying around and put them next to each other and added significant length to accommodate the tape I had and allow for some additional roles of different types in the future. The fat tape types like duct tape, packing tape and painters tape all have a hole in the middle that will be accommodated by the 3" pvc, and the electrical tape and tapes with a similar sized central opening will be taken care of by the 1.5" PVC... look at the picture, understand that the two types are separated by ~1" and adjust to accommodate whatever tape you have lying around plus some. Cut a bottom piece long enough at the full width of the fence slat. I made mine 22" long.
Step 2: Prep the Bottom
Once the bottom is cut to length it's time to prep that piece for the middle piece that will separate your smaller tapes from your larger tapes (smaller or larger in this context is based on the diameter of the tape roles center opening, not the tape width). There are a few options here. The easiest is to do nothing and simply cut and glue down this center piece in a later step. Given the amount of support it will have it should probably be fine. I drew parallel lines the width of a fence slat and routed a 1/4" grove to drop the middle piece into to give a little additional purchase and make it easy to glue down straight. You could also get fancy with this and do a dovetail for serious rigidity, but the final product here for me came out really rigid anyway. You're call on this, any of these you choose I see working out nicely... just make sure to mark your parallel lines so that all of your larger tapes will have room to fit with some to spare for future tape, in this case I made the marks about 2/3 of the distance from one side.
Step 3: Create Your Side and Center Pieces
For this operation I cut the center piece to 8" in length and stuck it in the previously routed grove on the bottom piece. Once that was in place (but not glued down or anything yet), I marked off and cut the two side pieces by holding them against bottom/center assembly as shown. This will ensure that once the side pieces are on they are the same height as the center piece even though their lengths are not equal because the center piece is in a router grove and the side pieces will be flush with the bottom.
Step 4: Mark the Middle and Side Pieces for Routing
In this step you are going to be marking the sides and middle for the slots that will ultimately hold the PVC your tape is on. Start with your two side pieces. Using a square mark 2" in from the top and 2" in from one side and then draw a line through those marks using your square so that you have a "+" sign. This plus sign will be what your PVC is ultimately centered on so you have to make sure that you set the pieces up in such a way that these plus signs/circles will be oriented towards the front of the dispensers... in order to keep everything straight. Just imagine an invisible straight line passing through each + sign and everything should be straight and level. For the center piece (the shorter of your three small pieces) you will still be marking 2" down and 2" over, but do so on both sides of the piece so that the imaginary line passes through both + signs without going at any kind of angle.
I used a miter saw to shave off small circles from my two different diameters of PVC for a an easy template. Center these rings on the plus signs you made and draw a circle around them. I just eyeballed this part, holding the rings down with my thumb and marking around them. The large + sign makes this pretty easy to do accurately enough for the tolerances involved here.
One of the end pieces will need a circle from your larger 3" diameter PVC and the other end piece will need a circle from the smaller diameter. The Middle piece will need a circle on both sides, one large and one small. Like I said, just visualize this whole thing put together and imagine an invisible straight line passing through the center of each circle.
Once you have the Circle marked use your square and draw straight lines from the outside diameter of the circle extending up to the top of the piece. To visualize, what you're trying to do is set up a perfect "U" shape that will be routed out in the next step.
Step 5: Route the Slots for the PVC
Use a router to bust out 4 "U" shaped slots where you marked them in the previous step. For the end pieces you can set your router to approximately 1/2 the depth of the wood. For the middle piece since you are routing it on both sides and don't want to just make some big fat open "U", make sure to set the bit depth to about 1/4 the board depth so there is a "U" on both sides but they don't show through to the other side. (Look at the picture of the finished project to get a visual on what I'm talking about if it doesn't make sense).
Step 6: Prepping the Front and Back
Cut a new piece the same length as the bottom piece. Once this is done rip this new piece in half lengthwise making two long slim pieces. Discard one of these, the one you keep will be the back of the unit.
Step 7: Glue and Screw
Now, either all at once or in stages use wood glue, clamps and a few strategically placed (pre-drilled!) screws to assemble the bottom, sides, middle and back piece. DO NOT glue on the front piece yet, (you shouldn't have made it yet, but just in case you got ahead of the game...) you will first want to put your tape cutting edge on it.
Step 8: Cuttin Some PVC
Now cut one 3" diameter piece of PVC and one 1" diameter piece of PVC (depending on what you started with and routed out for) to length measuring from the inside of one "U" to its opposing side so that the PVC can slide down into the slots as show in the picture below.
Step 9: The Cutting Edge
Now either rip a little bit more fence material so you have an approx 1" wide piece of wood the length of your assembled unit, or as in my case pick up a piece of junk wood from your garage floor that was already a good width and cut it to length. Attach 2 old jigsaw blades to this piece using some tiny nails or screws with heads big enough not to pull through the blade holes as shown making sure the teeth of the jigsaw are sticking up above the wood about 1/8" and clamp/glue/screw that piece to the front of your assembly.
Step 10: Optional: Side Post for Really Small Tape That Isn't Effective on a Dispenser Anyway
After I was done with the rest of the assembly I realized the only tape I had at the moment that had a small diameter opening that fit the small side of the PVC assembly was electrical tape at the moment. I also had a bunch of plumbers tape and double sided tape laying around that had an even small diameter, wouldn't fit on the assembly, and isn't the kind of tape you just pull a piece out of a dispenser for anyway. Plumbers tape would be useless out of something like this because of it's physical properties and the fact that it's almost exclusively used as a wrap. I still wanted all of my tape in one place so I took this little extra bit of dowel I had laying around and glued it to the inside corner of the small PVC side of the until and just threw all this tape on there for storage. Now I have a pretty sweet tape dispenser for all my tape and it all stays in the same place.
Step 11: Fin
The final product.