The way I built them, you'll need about 40" of 6x1 (or 24" of 10x1), 90" of 2x6, wood glue, as well as a band saw and a table saw to cut the wood to size, and a pneumatic staple/brad gun for assembly.
Step 1: Design
2.95" OD x 4.42" H
4.00" OD x 4.67" H
, so I made the boxes 6" wide, to hold two of the smaller cans side-by-side, and 4.25" wide, to hold a single row of the larger sized cans.
The height of the wider boxes is larger mostly for aesthetics, though when fully loaded, they do weigh more, so the increased moment of inertial (and thus strength) is a plus too.
Step 2: Cut
I needed 40 thin slats, 3/16"x1.5"x18", and 20 thick slats, 1/2"x1.5"x18". If some of your slats are slightly thicker than others, sort them by thickness and use ones with similar thickness on the same box.
I also needed 8 small ends, 4.25"x3.75", and 8 large ends, 6"x5.75", which I cut from the 1x10.