The news I have gotten is that earrings purchased or received within a few years may likely be replaced if the manufacturer is identified; however, if the earrings are several years old, that style may no longer be available for direct replacement. A first step which you have likely considered is to go to the business selling the earrings in the first place. That business would be most able to quickly identify the vendor and perhaps replace the missing one. Keep in mind, the earrings may only be available in a pair, not a single unit.
To identify the maker can often be difficult and I stopped trying to do that for questioners here at allexperts. Many makers are out there and much Cheap Shapewear is imported with various makers’ marks. Identification becomes almost the job for a detective armed with books and books of makers marks! To read the markings which are generally small on earrings, you will need to get a good 10x lens or go to a jewelry store with a microscope and ask if they can read the mark or let you have a look. Still, the mark if recognized by the jeweler will help but if unknown you are back to a difficult task.
If the earrings are precious metal, meaning gold generally and are not costume jewelry, there is a reasonable possibility of having one made. Costume jewelry simply cannot be duplicated by jewelers both because of the metals and finishes used and because cost to duplicate are high. If the earrings are precious metal, you do have a chance.
Since the jewelers you have visited did not seem interested in making or matching your earring, you should try a local business which sells quality jewelry but also has a bench jeweler working in-house. The business should also do custom work. The bench jeweler is the one who does repairs and makes custom jewelry.
Then, ask the clerks about replacing the missing earring and if they can order a “mounting” or similar earring from their vendors. If so, you are in luck! If not, the jeweler can look at the earring and see if that is an item they can make for you. Keep in mind; cost will likely be more than the original price since this may turn out to be one-of-a-kind work.
Often, a similar design may be purchased and the jeweler can modify to make the purchased earring match the original. This last approach is less costly than having the earring made from scratch. As last resort, try a jewelry business specializing only in custom work to have the item made. I would try that business last since many full service jewelers who do custom work have large vendor bases to check for an earring which may be purchased, avoiding the need of custom work. The jeweler who does strictly custom work will likely not have that vendor base to call upon.