One thing to be careful of: in some cases, applications using serial printers have roots going way back to before the concept of a general purpose printer driver(this was the norm, back in the DOS days, and persisted quite a bit longer in certain specialty applications). In these cases, the system had no knowledge of the printer; but whatever the specific application is would interact directly with the serial port, and use its knowledge of the appropriate printer language.
I ran into this not too long ago with a school system's grade reporting setup. The vendor provided a hardware/software bundle, with an application that pulled grades from the database, and dumped information to a custom serial printer that fed through report card forms. There was no printer driver as such, and I'm not even sure that the application supported "printing" in the modern sense. It may have been restricted to only talking to the accompanying printer.
If this is the case for your setup, then your options narrow considerably. You'll have to consult the app's documentation directly, figure out which serial printers(or serial printer languages) it can talk to, and work from there.
If the app is using the serial printer as an ordinary system printer, life is much simpler, just get any suitable modern printer and make the swap.
If it turns out that the app will only speak to a serial printer, and you can't get one at appropriate cost, you might have one other option.
http://www.softpedia.com/get/S...ous/PrintCapture.shtml came up for me when I was poking at your problem. It is a piece of software that emulates a serial printer in software, and outputs image files. If you combine such software with a virtual serial port driver(or, in a pinch, connect one of the computer's serial ports to the other with a null modem cable) you should be able to convert the output of the legacy app to ordinary images which can then be printed by any common, cheap, system printer. Exactly how easy this will be depends on the capabilities of the programs, and your comfort with scripting and automation; but this might be one of those problems better attacked in software than in hardware, seeing as serial printers aren't getting any more common or cheap as time goes on.