Look for information on concrete wall anchors. Attach your 2x4s to the wall with a few anchors (just like you would mount them to studs first), then screw in your dumbbell holders.

I would try one in the garage on a bare stud first, though, to make sure it will work. It seems to me like you'll have to put the hooks very close to the top of the board, and have the board stick out far enough to accommodate the "bell" part above and below. Getting that distance right - enough room to hang the barbell, and enough board to support the screw - might be the tricky part.

I have four dumbbells, and made a basement rack out of 3/4" plywood for them. Two of my three barbells are downstairs. But it turned out that I really needed two dumbbells upstairs. I have not made a rack for them yet.

I already had many wood DIY shelf units, so a space was found between two existing shelf units that was just large enough for the barbells. This way I did not have to worry about attaching to a wall. I just screwed two pieces of plywood to the existing shelves. They already had four cut outs for my four dumbbells to be slip into. Six screws did the trick, it rests on the floor.

My dumbbells are the Wal-Mart screw on type that take plates.
Since I keep wood scraps it didn't cost anything to make the rack.

that should read --

,... was just large enough for the dumbbells.

Thanks for your responses.

Of course after having given up on finding an inexpensive store-bought rack and presenting my idea here for a DIY one, I recently found a reasonably priced ready-made rack that'll likely work.

I will save our efforts for finally installing our gladiator garage storage system. We bought the parts last November and it suddenly turned too cold to work in the garage. Our main challenge is securely fastening the gear track to our hollow cinder block garage walls. I believe my boyfriend found an anchor type product that will work, but I'd feel better if we also used some construction adhesive to boot.

hooray for finding something ready-made and reasonably priced!

Good luck with the storage-system installation!

Oh, I was going to say--if you still needed to make your own rack--you could screw those hooks into a piece of 3/4"-thick plywood and then just lean the plywood against the wall. Put rubber feet on it, or something.

Or use a couple of door hinges to attach two pieces of plywood or board into an A shape, and put the hooks on either side. Then it would stand alone (you could attach a chain inside or use cross braces to keep the A shape from moving around.