...My father picked these up on a trip to Syria....
Right there is the biggest reason to doubt these coins.
Syria, like most countries in the Middle East, has quite strict
Antiquities Laws that prohibit the casual sale of ancient artifacts, including coins.
Click here to read them.
Now I have no idea how well these laws are actually enforced, but professional coin smugglers would never take the chance - after all, the "tourists" could just as well be government agents. They'd get more
money and stand less chance of getting caught by smuggling them out of the country themselves.
Genuine
ancient coins are rarely sold to tourists on the street, anywhere. They will often have a story about how they found them, or even take you off to a ruin "nobody else knows about" where there are
ancient coins just lying around for you to
pick up. In all cases, these "coins" will be recently made
fakes.
OF course, countries with strict anti-looting laws normally have no problem whatsoever with people making and
selling fake ancient coins, so what these folks are doing is perfectly legal there. One hopes that the government agents and customs inspectors are sufficiently well-trained to spot
fake ancient coins when they see them. Otherwise, a tourist could be hauled off to jail or pay a hefty
fine for trying to "export" the
fakes.