I think gabardine and other suitings are acceptable as covers; but they don't STRETCH. You'd also need to add a soaker panel, of something beefier like sweater knit or flannel. I think they make great daytime dress-up covers. They're just not as absorbent as traditional diaper cover woolens. I've used suiting as the outer layer and something more absorbent (flannel, knit) for the inside and gussets.
The only thing I won't use is scratchy things like tweeds et al.
Basically; anything that is soft, at least 90% wool, preferrably slightly stretchy and can be lanolized will work! imho.