I would assume that cloth was commonly used for nonmilitary tents (in fact... naaah, can o'worms, not going there
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I did my first Roman even this past weekend as a field cook under an improvised awning. We based the setup on images from the Pompeii arena riot fresco which shows awnings suspended between four vertical poles, presumably itinerant sales stalls or popinae. That is the direction I would go. The most likely material IMO would be linen (better waterproofing qualities for weight and bulk) and the most likely colour off-white to brown, as dyeing linen was a relatively expensive proposition. Unless you have permanently installed poles you need guyropes which the fresco doesn't show, but I assume that was simply done to avoid visual clutter.
In the absence of heavy rain (which we didn't have) and chill wind (which, unfortunately, we did), an awning like this is quite comfortable, creating an enclosed space, shade, and a modicum of privacy. You can (but I did not) fold down one edge to make a 'back wall', and a similar rectangular cloth (or the same, if you're willing to go through the trouble of doing that every day) can be placed over a simple tent frame to make the kind of A-frame tent seen in the Vienna Genesis and Ambrosian Illiad. Yes, these are late antique sources. Can't give you better than this.
The thing is, I suspect Roman traders would not normally have used a tent. Travelling within Italy or the more civilised provinces, they could fall back on an established network of inns and waystations for accomodation. Travelling into the less civilised areas, they are more likely to be going by ship or wagon asnd thus already have a place to sleep. The only people I could see sleeping in tents are traders coming to very big events (festivals or such) where accommodation can't be had, or those going overland with mule trains. In either case, a tent could just be improvised from any large piece of cloth and available sticks and/or
anchoring points, as was commonly done until the twentieth century by itinerants.
EUR 0.02