There are lots of ways this can be done and I'm working on a couple of others already, but this method originally fired my imagination.
All these parts and the hotair gun came from the same mega-hardware store and should be readily available at your local store also (or parts that can substitute). Since building this diverter, I've tried PVC pipe moulding and could undoubtedly build this even cheaper. To find the parts I just played around with bits in the store that fitted or were close.
DISCLAIMER: heating PVC releases toxic gasses. Either use a respirator or work in a properly ventilated space. If you don't take adequate precautions with this or any other project, only you are responsible! Same applies to power tools, eg the business end of a hotair gun is HOT!
Downpipe T-junction ("Downpipe RJ80WH junction 95' 80mm WHT" $9.84)
Large reducing bush ("Socket red bush 124-80-50" $19.47)
Small flashing cone 50mm - 32mm. ("Cone flashing 131-32" $5.38)
HDPE elbow ("Elbow female HD 20mm RXFE20" $14.84)
Interior flashing cone 80mm - 50mm (This is not on the receipt, so maybe I didn't get charged for it! About $6.00?)
Waste pipe ("Pipe waste optim 100.50.1 1.0m" $22.40) [125mm = $2.80]
PVC pipe cement [already on hand]
That's $58.33. Secondhand parts or a different construction method would greatly reduce this.
Tapemeasure (or ruler)
Step 1: Interior Overflow Assembly
2 Poke a tape measure down from the flanged end and hook it on the shoulder of the flashing. Take a reading where it comes out of the flanged end and subtract 2.5cm (1 inch) - this is the length of 50mm pipe you'll need. Don't be too pernickety with this: it is more important that whatever length you choose, the top of the overflow is level with the maximum height of the water in your tank. This is determined when you fit the diverter to the downpipe on your house.
3 After sanding off the cut end of the pipe, glue the pipe into the flashing so it is flush (level) with the bush's shoulder. Again, not critical but make sure that the top of the overflow pipe is shortened to be about 2.5cm below the T-junction flange.
4 You could glue the overflow assembly into the T-junction, but as it is a very snug fit I've left mine unglued for now until I see how the diverter handles detritus.
Step 2: Outlet Assembly
2 Soften the large end of the small flashing cone until it is quite soft then carefully force it into the 50mm hole in the large bush. This is a tricky step so take it slowly. You'll end up with a shape that tapers rapidly from the cone's shoulder to a 50mm outside diameter ("OD") tube. Don't glue this in just yet.
3 Soften the small end of the cone the same way as for the T-junction flange, and insert the elbow using the same technique as for inserting the bush.
4 Glue the cone into the bush, and the elbow into the cone (you can't use PVC cement, so this is where the hotglue gun comes in). You could glue the bush into the T-junction, but for me it is a very tight fit and leaving it loose means I can pull out the outlet assembly should I need to clean out the diverter without taking it off the downpipe.
Step 3: Fit Diverter to Downpipe
I'll take some pics and create another Instructible showing the installation process .
Oh BTW, if you like deforming PVC go check out Thinkenstein's stuff! And trevormates' "PVC 101".