Yeah, I don't know how to weld, but I do know how to kludge!  This trailer will take you less than 30 minutes and under $10 in parts if you can get a used trailer that someone is tossing out.  (Try craigslist or freecycle.com for people getting rid of the old, ripped up trailers.)

Take any kid-carrier bike trailer and strip off all the moldy fabric.  You can leave as much or as little as you want.  The one we got had pretty solid bottom fabric, but the rest was yucky!  You can just cut it off with scissors or a utility knife.

Then measure the width of the trailer between the rails, run to the hardware store and buy one of those wire shelves that they carry for closet remodeling.  Make sure the length is twice the width of the trailer.  (Ours cost less about $5.00.)  Also pick-up 8 pipe clamps (a bag of them cost less than $1.50).  For cheap but less sturdy, you can use zip ties.

Back home, remeasure the width of your trailer, making sure that your measurements keeps you from hitting the wheels but allow the shelf to rest on the trailer rails.  Using a hack saw, cut your shelf into the measured lengths. 

Place the shelves on the rails and make sure the ridge is pointing up so the shelf is flat on your rails.  Then zip tie or pipe lamp the 4 corners of the first shelf to the bike trailer rails.  When done, put the next shelf in and make sure the ridge is at the opposite end from the other shelf.  Attach the corners of the second shelf to the rails.

And ....that's it.   You're done.