There are a few options open to you, a robotic script on the FM Desktop to handle the iOS print Jobs or a Lantronix Print server to allow your iOS devices print to any printer.
It is well discussed in this thread Printing with Star Micronics POS Printers
Look at https://www.decisivetactics.com.
They have a product called Printopia that is a control panel that runs on a Mac. It turns that Mac into an AirPrint server so you can then print direct from any iOS device. The Lantronix hardware print server mentioned in the other reply is also well regarded.
I've also had success using handyPrint which costs just a $5 donation - as with printopia, it enables airPrint capabilities to printers connected to your Mac.
You can get it here: Netputing » handyPrint v5
printopia (among other products) is cool - we print even labels on a Brother QL500 Labelwriter from iPhones. IMHO the easiest way - as long as the printing dialog is no problem (on iOS, the printing dialog will appear, IMHO no way to print 'without dialog')
There are some ways to print 'without dialog', in addition to using the 'robot' FMP client method:
I've been able to generate PDFs of the intended print output within FileMaker Go, and then convert that PDF to base64 which is then sent to a php script on a web server using Insert from URL and httppost.
The php script can then do things such as send it to Google Cloud Print (though I found there were sometimes delays with that), or if running the web server on a local network Mac, the php script could decode the base64 back into it's PDF file and save it into a folder with Automator's 'Folder Actions' set up that then prints the PDF automatically... Works nice :-)
Ditto on Printopia.
It can also print to the Desktop of a Mac or to Dropbox.
Effectively takes any non-Airprint printer (like label printers or older inkjet or laser printers) and makes it an AirPrint printer.