If you don't have access to stdbuf, you might as well simulate it and unbuffer the stdout manually with gdb (assuming obviously you have access to gdb).
Let's take a look at how stdbuf actually operates. The stdbuf GNU coreutils command basically only injects libstdbuf in the user program by setting LD_PRELOAD environment variable. (Irrelevant, but for the record, options are passed via _STDBUF_E/_STDBUF_I/_STDBUF_O env vars.)
Then, when the libstdbuf is run, it calls setvbuf libc function (which in turn executes the underlaying syscall) on appropriate file descriptors (stdin/stdout/stderr), with the appropriate mode (fully buffered, line buffered, or unbuffered).
Declaration for setvbuf is in stdio.h, available with man 3 setvbuf:
#include <stdio.h>
int setvbuf(FILE *stream, char *buf, int mode, size_t size);
Values for mode are: _IONBF, _IOLBF, _IOFBF, as defined in stdio.h. We are here only interested in the unbuffered mode: _IONBF. It has a value of 2 (you can check your /usr/include/stdio.h).
Unbuffer script
So, to unbuffer a stdout for some process, we just need to call:
setvbuf(stdout, NULL, _IONBF, 0)
We can easily do that with gdb. Let's make a script we can call, unbuffer-stdout.sh:
#!/bin/bash
# usage: unbuffer-stdout.sh PID
gdb --pid "$1" -ex "call setvbuf(stdout, 0, 2, 0)" --batch
Then, we can call it like:
$ ./unbuffer-stdout.sh "$(pgrep -f my-program-name)"
(You'll probably need sudo to run it as root.)
Testing
We can use this simple Python program with buffered standard output (if not called with -u, and with unset PYTHONUNBUFFERED), writer.py:
#!/usr/bin/python
import sys, time
while True:
sys.stdout.write("output")
time.sleep(0.5)
Run it with:
$ ./writer.py >/tmp/output &
$ tailf /tmp/output
and observe no output appears until we run:
$ sudo ./unbuffer-stdout.sh "$(pgrep -f writer.py)"