Finally decided to make one myself by getting an Ikea Malm 4-drawer chest, and building a removable attachment for the changing pad.
Highlights of this project: Can store diapers/wipes/etc out of sight in the top drawer.
The top is removable so when you don't need a table, you have a normal chest.
The particular pad used, is from Target and had straps to secure it to a table. Attached it to the removable top, and the screws don't damage the plywood.
The height of this is a bit higher than a standard changing table, but this is actually preferable for me because I am 5'9" and my husband is 6'5". If you do something similar yourself, keep the height in mind.
I didn't bother painting it but it would be easy enough to spraypaint.
Step 1: Get a Changing Pad
It turned out this pad also had two nylon securing straps on the back, which came in handy for permanently attaching it to the removable top.
Step 2: Cut a Top and 3 Side Rails to Fit Chest
The flat part of the table top needed to be at least 1/2" thick, in order to screw the side rails into it.
I cut the side rails to the depth of the chest so they would line up when seen from the side. The back rail, I used a scrap piece of 1/2" plywood to minimize the distance from the wall, and also gave it a significant drop behind the chest (about 6"). I determined I didn't need a front rail because the top wouldn't slide around with two sides and the back support wedged against the wall.
I cut the flat plywood top the same dimensions as the chest top. To allow me to screw the sides into it, and also so spills/messes would go on the top and there would be some protection for the chest top. I accidentally cut it 1/2" short on one side, and solved this by cutting an additional 1/2" strip and screwing it onto the side.
Step 3: Screw Side and Back Rails Into the Top
The side rails went below the top about 1.5", which held it securely on the top of the chest.
To attach the side rails, I first drilled 1 pilot hole through the rail near one end. Then I put the drill bit through the hole and held the rail next to the side of the tabletop, so I could continue the pilot hole into the side of the plywood. This was important because 1/2" is a narrow target. By continuing the pilot hole, it helped the screw go into the right spot and not be tilted and potentially angle down into the chest, or up into the changing pad area.
Because the rail happened to be pretty deep, I also drilled countersink holes at the outside of the rail. These allowed me to use a slightly shorter screw, and then later I can fill the holes with wood filler if I feel like it.
I screwed the first screw into the rail, a little loose so the rail could be rotated a little. Then I held the rail level, and marked the position of top of the plywood on the inside of the rail. I decided to use 3 screws total across the rail.
To make the remaining 2 pilot holes, I rotated the rail up and drilled from the -inside- of the rail, just below the mark.
note in the drill picture from the inside, I took this photo after it was assembled. So I just am showing how low below the mark, to drill the inside of the rail.
Once those were drilled through, then I put the drill bit in from the -outside-, rotated the rail so the bit went to the center of the side, and continued the pilot hole. Did this for the end hole and then the center hole. Drilled countersink holes, then screwed the second screw into the outside end hole, and the 3rd screw into the center.
Repeated this for the other side, and the back.
The gap between the top of the chest and the plywood is because my piece of plywood was a bit warped. Despite the warping on one corner, the drop from the side and back rails kept the top from sliding.
Step 4: Attach the Changing Pad to the Top
Step 5: Set Top Onto the Table and Slide Chest Back to Wall. Done!
I tried putting a thin ikea dishcloth under the top to help prevent any sliding from scratching the chest top. It created a gap, but I'm going to leave it like that anyway to try to avoid wearing down the finish of the chest top.