It should work like this:
/usr/bin/program << EOF >/dev/null 2>&1
The program has three redirections defined for it. stdin is the heredoc, stdout is /dev/null, and stderr is set to the same place as stdout, also /dev/null.
If that doesn't work for you, and I can't see how it wouldn't, please show us what it's really doing in more detail.
Another possibility is to wrap the whole thing in a program group, function, or subshell and redirect that.
/usr/bin/program << EOF
} >/dev/null 2>&1
Edit: see here for more on how redirections work:
redirections and file descriptors explained