Prism99

Because the quilt is an even number of blocks across (8 blocks) and you are using 4 fabrics, I think there is only one way to avoid diagonals and avoid having the same colors next to each other. It would involve repeating the same 4 fabrics, but shifting over by 2 on each new row. Let me see if I can explain.

Number your colors 1 through 4. In row 1, fabrics will be 1-2-3-4-1-2-3-4. In row 2, fabrics will be 3-4-1-2-3-4-1-2. Those two rows will be repeated throughout the quilt.

If you change the quilt to 9 x 9, there are other possibilities. For 8 x 9, I think this is your only choice if you don't want diagonals and don't want the same colors next to each other . I did a quick work-up of this in EQ and the result is pleasing. It is similar to a woven effect.

Edit: I realized there is one other way to arrange the blocks. This would be Row 1 fabrics 1-2-1-2-1-2-1-2 and Row 2 fabrics 3-4-3-4-3-4-3-4. I do not find that arrangement as attractive as the first because there is less alternation for the eye, but it may work for different colors than I selected for my trial.