Thanks for all the input everyone. Back to the drawing board!
As I read this, I am looking at a coffee table I built about 45 years ago. It has a skirt all around made of 1x4 inch oak. The skirt boards are mitered into each other, but butt ending would have worked as well. The legs are 2x2 posts and are attached to the skirt by glue and pegs. The pegs were cut from 1/4" birch dowels. There are 8 in each corner, 4 of the skirt boards into each other and 4 into the legs, that is 2 into each side. It has lasted 45 years and shows no wobble. Of course, stability is not an issue since it is 40x40 and maybe 20" high.