@bmike gave me most of what I needed.  A few additional clues and limitations.

Emacs is an app that lives in /Applications/Emacs.app and it has lots of stuff within that directory.  I finally took it one step at a time.  I created a `dumpme` app:
```
#include <unistd.h>
#include <signal.h>

int main(int argc, char *argv[])
{
  pid_t pid = getpid();

  kill(pid, SIGBUS);
}
```
and I did the `codesign` as suggested and I got a core file.  Note that before the code side, I would get
```
zsh: bus error  ./dumpme
```
and after the `codesign` I would get:
```
zsh: bus error (core dumped)  ./dumpme
```

A preliminary step in building the `Emacs` app is `temacs` which is an executable without an initial state.  I `codesign`ed it and it produced a core too when started from the `Terminal` prompt.  Then I did the `codesign` for `/Applications/Emacs.app/Contents/MacOS/Emacs` and I got this nastygram:
```
codesign -s - -f --entitlements tmp.entitlements /Applications/Emacs.app/Contents/MacOS/Emacs
/Applications/Emacs.app/Contents/MacOS/Emacs: replacing existing signature
/Applications/Emacs.app/Contents/MacOS/Emacs: code object is not signed at all
In subcomponent: /Applications/Emacs.app/Contents/MacOS/Emacs.pdmp
```
A search found [this](https://stackoverflow.com/q/29076321/341980) answer so I backed up and I did `sudo codesign -s - -f --deep --entitlements tmp.entitlements /Applications/Emacs.app` -- (Note the addition of `--deep`).  Also, without the `sudo` I got permission problems.

If I start Emacs from the `Finder` or via `open /Applications/Emacs.app` and kill it, I do **not** get a core file.  But if I start it from my `Terminal` prompt I do.  e.g.
```
% /Applications/Emacs.app/Contents/MacOS/Emacs
```

I suspect there is a fix when starting from `Finder` as well.  I'm assuming it has something to do with the `ulimit -c unlimited` that is suggested / required.

Update:

Take Finder out of the equation.  Get the app to set the limit itself.  i.e.
```
#include <unistd.h>
#include <signal.h>
#include <sys/resource.h>
#include <stdio.h>

int main(int argc, char *argv[])
{
  pid_t pid = getpid();
  struct rlimit l;
  int ret = getrlimit(RLIMIT_CORE, &l);

  printf("getrlimit returned %d\n", ret);
  printf("rlim_cur = %llu\n", l.rlim_cur);
  printf("rlim_max = %llu\n", l.rlim_max);
  l.rlim_cur = l.rlim_max;
  printf("setrlimit returned %d\n", setrlimit(RLIMIT_CORE, &l));
  printf("Time to kill myself\n");

  kill(pid, SIGBUS);
}
```
A modified Emacs.app even when started from Finder now produces a core dump.