Springs! I used part number 1692K45 but I think the 3 inch would have been better.
Ball Joints! I used the 1/2x20 for the trailing arms and 3/8x24 for the lateral bar. I like the ones with grease fittings but they do make a mess. I have no idea how long a sealed or nylon set would last, probably a very long time. Personally I like knowing I can pump fresh grease in and force all the nasty out. Keep a rag handy to wipe them off as extra grease attracts dirt.
Threaded Rod! They have stronger stuff but I don't see why you would need it. You can also use their stainless but I just painted mine. I bought two 3 foot sticks of 1/2 20 thread (you have to match the thread to the ball joints you find, whatever they are) I used one stick for the axle and another cut for the trailing arms. Starting over I would use 3/8 for the trailing arms, 1/2 is overkill. I would buy one 3 foot 1/2x20, one 3 foot 3/8x24 and one 2 foot 3/8x24. That would give you lots of flexibility in mounting your axle.
WHEELS! I got these from Northern Tool. You could source your own if you needed to. I used 16 inch but have thought that 12 would have been fine and kept the cart lower to the ground. Starting over I would go with the 12's unless you are planning on some serious off road, but if you are remember it will tip over. I wish I could find dust covers for them, I have found some neoprene rubber pipe caps with a 2" ID that I think will fit over the hubs. That would at least seal the wheels some. You would have to cut a hole in the inside one for the axle and the outside one will have to fit over your mounting system. McMaster only sells them individually and they are pricy at $4.66. I have not bought them and can not vouch for their effectiveness. I think I would try a local hardware or home center first but I included the part number for McMaster anyway.
SOURCE Protective Caps Part No. 2394K12
This has been a great build. My son loves it and we have done 100's of miles in the original. I decided to rebuild the unit to what you see here because my original suspension design allowed the axle to hop more than I like. It was unnecessarily heavy duty and any weight I could shave off is good. This new rear set up is both more efficient and lighter weight. You can see the build log here: Bike Trailer and I have all the sources I used for the few purchased parts there and above.