I've heard of people detecting in Panama. Here's some examples:
Bocas del Toro, Panama - Friendly Metal Detecting Forums
http://www.treasurenet.com/forums/other-countries/320389-republica-de-panama.html
(notice one guy only alludes to the govt. going to want any pre-columbian artifacts you may find. But not forbidding the actual finding of them, and CERTAINLY not anything to do with fumble-fingers tourist beach modern stuff. So I'm not sure why that particular city there, would be any different. You're talking about the tourist beaches that are right there, right in Nombre De Dios, right ? If so: detectors are a common site on tourist beaches all through Mexico, South America, Caribbean, etc....
If you're still worried: Is your city's laws/rules written somewhere for public viewing? If so, check them out. If nothing there says "no md'ing", then presto, it's not prohibited. Also if there's dealers down your way, they can let you know where their customers are using them. All the major manufacturers (Whites, Garret, Minelab, Fisher, etc...) have dealer listings. Just find out if there's any in Panama, or even neighboring countries who have sold to Panamanians.
Oh: And let's say that you found something dire sounding: Just make sure it's not something that only applies to shipwreck salvor stuff, or raiding pyramaids, etc... People have been known to ask bureaucrats/border layers/consulates a bunch of questions, and then being shown stuff like that. Yet in actual practice, have nothing to do with small-time hobbyist detecting. I mean, that would be like asking an archie in the USA, and being told "not allowed anywhere here", because perhaps he's thinking of Mel Fisher atocha legal hassles, or ARPA, etc..... So sometimes you need to read between the lines of what you are told, to make sure it's not something silly and not applicable like that.