You can go ahead and "code music in" on a C64 because it has a synth chip inside and if you pokedata to registers in the memory map, they make sounds. If you get used to it, you can make a pretty good job at it (Jeroen Tel). Even if you are not a programmer, if you know the right registers and how to use them and in which order, you can make a tune this way.
I am pretty sure that is not how the Amiga works, since it's DAC based. You'd have to add code to generate synth sounds or samples and it becomes a lot less trivial. LEt's not forget you can add data to the C64 memory right away through its inbuilt BASIC interpreter, and this just doesn't happen with the Amiga. Far easier, if you know how to code, to build an editor/tracker, and that's what some people did.
On another note, "Softsynth" software of note for the Amiga was Aegis Sonix, and some trackers synthesized their own samples to work with (AHX, SIDtrackr, Musicline, some versions of Octamed and more).
So in brief, although doing this on the C64 and other computers was a relatively "easy" way to get to do music for the computer, on the Amiga it wouldn't be as easy and I wouldn't see anyone doing it in its timeframe for practical reasons.