As long as you have the device identifier of the PCI-MIO-16XE-50 set the same as the PCI-MIO-16XE-10 for which the program was written, you shouldn't have a problem doing what you describe.
One thing that confused me about your posting, however, is the statement When downloading the executable files, Measurement and Automation Explorer gave a message that the physical devices could not be located. This doesn't make sense to me. You're getting an error from MAX when downloading your program? MAX shouldn't be involved at all here, and especially not when just downloading your program. If you can provide more details about exactly what you are doing (maybe post some screenshots) then I'm sure we can help you get your program working.
Good luck,
Joe