Old UA
Phoenician Heritage
+125

Goldwhen founding Cities, scaling with Era.
All owned Coastal Cities receive a free Lighthouse.
The

Trade Route Resource Diversity modifier is either doubled if the value is positive or halved if negative.
New UA
Okay, so free Harbor that provides city connections sounds pretty good.
The Trade route stuff is fine, I guess. Just generally a bonus that works away under the hood, without taking much real notice of. I can't really say how much if a impact it has.
Well I think the gold on settle, is somewhat boring and means a steep drop off in terms of bonus. Instead I propose a different idea. Instant gold yield upon first connecting a luxury (and maybe also strategic) resource, and also upon obtaining a monopoly. Resources from city states count for instant gold yield, but trading with civs does not.
So this instead grants instant gold bonuses, in a more spread out fashion throughout the game. More so if you keep expanding, either territorially or diplomatically. But even if you stay small, you get you nearby resources, your monopoly and the strategic resources as they unlock in tech.
Now historically, Tyre and Carthage were involved in a lot of trading monopoly on the Medditerrian, so it fits historically.
And it keeps the same general idea for their UA, without going into big later changes.
I think you do not take into account the nature of ancient states. There was no direct centralization of power or effective means of exercising unity or control over vast territories so all those ancient empires were functioning more like a central capital or province which it had direct control of, and other regions which functioned more like puppets or city-states, not annexed and fully legally, economically, or socially integrated territories. It was not only the Carthaginians but most of ancient nations that had not direct unified, standing army (before late Rome and Martian reforms) and wielded only some native troops, the rest being allies who had they autonomy. It was the same in Rome, the same in Greece or Macedon's holdings and, of course, Alexander's army, the same in Persia and later Hellenistic Diadochi empires. Rome functioned the same as Carthage with alliances, treaties and occupations of other territories and cities around the Italian Peninsula, some of which switched to Carthage side like Capua. Roman Army were also mostly composed of those allied troops and Roman state. The same with Roman state, different constituencies provided different artisan's products, taxes, harvests, and of course troops during wartime and allegiance. Definitely Carthage did not had only one division of land forces though, though as with contribution of Eternal City, it remained small contingent of troops amid the masses of levies from allies and directly controlled rural territories. Alexander's army? Some Macedon core and other main Greece allied city-states, the vast majority (increasing towards the end of his conquests) other Asian Minor Greek allies, levies from conquered Persian lands, mercenaries.
My point was that Carthage maintained a extremely diverse army, in terms of both culture and fighting styles, which was still effective. Rome on the other hand using them as a example, had it allies either follow the Roman model in terms of infantry, or just cover their military gaps in doctrine, such as cavalry. Rome was more 1 Roman legion, 1 auxiliary formation in general.
Back to the Cavarnsary. My point about the map, was a edge case one. But this is basically a less dumb version of justifying the base Civ5 Indonesia UA. Hey Indonesia was a bunch of islands, so anything that isn't is just ahistorical. And if you don't like that, than just don't play them or have them be a AI on all these maps. (Which means I need to pick AIs and can't allow some randomness). Having a Cavarnsary for inland cities still makes them absolutely worse than more coastal ones. But it makes the weakness just a tad less, and makes them more functional if they roll a bad spawn on maps, with coastline. Like being forced inland, on the other game I mentioned. Which was the main point.