Carbon apps do run on current Macs, and on the current macOS (10.14). But that's the end of the line. Carbon is 32 bit only, and Apple has announced they are dropping 32 bit soon.

It's not actually. Only the UI parts of Carbon are deprecated:

"We are still planning to support the Carbon Event Manager and Text Input Sources, to name two mostly non-UI APIs. You might wonder, what about the Memory Manager, or the Alias Manager, or the Process Manager, or other lower-level managers? At this time, it looks like most, if not all, of the APIs provided by the ApplicationServices and CoreServices umbrella frameworks will still be available in 64-bit." - Eric Schlegel (apple developer)

You could reimplement Carbon in Cocoa.