I'm glad I'm not annoying - as I've said before I really hate being overly critical, but I wouldn't do it if I didn't think the rest of your civs are top tier in terms of design. It'd be a shame to me if one civ lagged behind the others in my eyes, so I have to speak up when I see it (so take it as a compliment really!)
Personally the only bit I think that needs a
total overhaul is the UA, the Corsair and ribat both work but might need a few tweaks to fit a new UA. For the UA, if you want to keep coasts, desert and faith, with some trading stuff, how about..
UA: Barbary Corsairs
Merchant specialists yield +1

faith and +1

food in cities with a naval garrison, rising to +2

faith and +2

food in desert cities. Whenever a

Great Merchant is born,

level up all your naval units.
Hafsid Tunis was kept alive by the fact that the profits of international piracy and the subsaharan trade networks both flowed directly into the pockets of Tunisian merchants. The Naval garrison references the way piracy and plunder brought immense wealth (and, of course, slaves) into Tunis, whereas the desert boost references how immense amounts of invaluable gold, salt and ivory found its way into Tunisian markets from beyond the Sahara. Both of things contribute towards merchants which yield urban growth (food) and ordered, well kept markets. (maintaining well kept markets are a religious duty in Islam, weirdly, hence the faith) Then there's the second part of the UA, which references all those famous corsairs who made a loot of money through the trade - half merchant, half pirate hero, passing on their skills to all your units. The two bits also work together really well, working lots of merchants will level up all your naval units and also allow you to survive and thrive in the desert.
So with that new UA, I'd only suggest a couple of tweaks to the other bits.
UU: Corsair (Replaces Galleas?)
The Corsair earns additional

experience the further it is from the

Capital, unlike the galleas it replaces, and inherits some of the experience from units it kills, allowing it to level up extremely fast to offset its inherently weak strength when compared with the regular galleas. When garrisoned, the Corsair yields +2

gold and +1

great merchant point for every level it has accrued.
This corsair takes advantage of both of Regalman's experience focused ideas to make for a unit which can level up extremely quickly to get past the fact that it is much weaker than the regular galleas. Tunisian sailors were extremely competent, which is how they managed to remain relevant even when their smaller xebecs became outclassed by European warships in the 18th and even 19th centuries hence the way these ships rely on experience over brute strength. This also synergises with the UA, as you can get even more experience from the great merchants you generate - and then generate even more great merchants during peace time in order to continue the cycle. In short, keep warring for some pretty insane monetary buffs - very similar to the real Tunisian pirates.
Now I liked the ribat, and don't think everything necessarily needs to be about synergy, but I wasn't convinced by the way it encouraged land trade far too much when Tunisia should focus more on the coasts. So just a tiny tweak needed.
UI: Ribat (Available at currency)
The Ribat yields +1

gold and +1

faith, and yields an additional +1

science and +1

faith after researching education, however it may only be constructed on desert tiles. Crucially, whenever you send a

trade route from a city, receive

science for every worked Ribat in that city.
Shifted the yields around a bit to make up for the removal of the caravan mechanic, now making it staggered instead so the extra science isn't too overpowered. I worried about the yields here but realised quickly that the main two yields that desert tiles sorely lack which other tiles have, food and production, aren't yielded by this improvement, so it needs to be pretty strong to make up for that. Ribats were centres of learning, but also centres of faith, so the extra faith accompanying the science not only makes sense, but also ties together nicely with the small amount of faith in the UA to give the entire civ that slight faith focus you wanted in the original.
Overall then, a money focussed pirate civ which makes the most out of coastal deserts. What'dya think?