The init.d/openresty file for Amazon Linux (and probably redhat linux families). Just based on the default init.d/nginx (that comes from a standard "yum install nginx"

init.d-openresty.sh

#!/bin/sh
#
# openresty adapted script to start and stop the openresty compiled
# nginx daemon

# --- original nginx comment ---
# nginx - this script starts and stops the nginx daemon
#
# chkconfig:   - 85 15
# description:  Nginx is an HTTP(S) server, HTTP(S) reverse \
#               proxy and IMAP/POP3 proxy server
# processname: nginx
# config:      /etc/nginx/nginx.conf
# config:      /etc/sysconfig/nginx
# pidfile:     /var/run/nginx.pid
# --- /orginal nginx comment ---

# --- openresty comment ---
# override config with the default open resty location
# config: /usr/local/openresty/nginx/conf/nginx.conf
# config: /etc/sysconfig/openresty
# pidfile: /usr/local/openresty/nginx/logs/nginx.pid
# NOTE: need to go to the openrest/nginx/conf/nginx.conf and uncomment
#       the "pid   logs/nginx.pid"
# --- /openresty comment ---

# Source function library.
. /etc/rc.d/init.d/functions

# Source networking configuration.
. /etc/sysconfig/network

# Check that networking is up.
[ "$NETWORKING" = "no" ] && exit 0

# nginx original:
# nginx="/usr/sbin/nginx"
# openresty new value:
nginx="/usr/local/openresty/nginx/sbin/nginx"

prog=$(basename $nginx)

sysconfig="/etc/sysconfig/$prog"

# nginx original:
# lockfile="/var/lock/subsys/nginx"
# openresty new value:
lockfile="/var/lock/subsys/openresty"

# nginx original:
# pidfile="/var/run/${prog}.pid"
# openresty new value:
pidfile="/usr/local/openresty/nginx/logs/nginx.pid"

# nginx original:
# NGINX_CONF_FILE="/etc/nginx/nginx.conf"
# openresty new value:
NGINX_CONF_FILE="/usr/local/openresty/nginx/conf/nginx.conf"


[ -f $sysconfig ] && . $sysconfig


start() {
    [ -x $nginx ] || exit 5
    [ -f $NGINX_CONF_FILE ] || exit 6
    echo -n $"Starting $prog: "
    daemon $nginx -c $NGINX_CONF_FILE
    retval=$?
    echo
    [ $retval -eq 0 ] && touch $lockfile
    return $retval
}

stop() {
    echo -n $"Stopping $prog: "
    killproc -p $pidfile $prog
    retval=$?
    echo
    [ $retval -eq 0 ] && rm -f $lockfile
    return $retval
}

restart() {
    configtest_q || return 6
    stop
    start
}

reload() {
    configtest_q || return 6
    echo -n $"Reloading $prog: "
    killproc -p $pidfile $prog -HUP
    echo
}

configtest() {
    $nginx -t -c $NGINX_CONF_FILE
}

configtest_q() {
    $nginx -t -q -c $NGINX_CONF_FILE
}

rh_status() {
    status $prog
}

rh_status_q() {
    rh_status >/dev/null 2>&1
}

# Upgrade the binary with no downtime.
upgrade() {
    local oldbin_pidfile="${pidfile}.oldbin"

    configtest_q || return 6
    echo -n $"Upgrading $prog: "
    killproc -p $pidfile $prog -USR2
    retval=$?
    sleep 1
    if [[ -f ${oldbin_pidfile} && -f ${pidfile} ]];  then
        killproc -p $oldbin_pidfile $prog -QUIT
        success $"$prog online upgrade"
        echo
        return 0
    else
        failure $"$prog online upgrade"
        echo
        return 1
    fi
}

# Tell nginx to reopen logs
reopen_logs() {
    configtest_q || return 6
    echo -n $"Reopening $prog logs: "
    killproc -p $pidfile $prog -USR1
    retval=$?
    echo
    return $retval
}

case "$1" in
    start)
        rh_status_q && exit 0
        $1
        ;;
    stop)
        rh_status_q || exit 0
        $1
        ;;
    restart|configtest|reopen_logs)
        $1
        ;;
    force-reload|upgrade)
        rh_status_q || exit 7
        upgrade
        ;;
    reload)
        rh_status_q || exit 7
        $1
        ;;
    status|status_q)
        rh_$1
        ;;
    condrestart|try-restart)
        rh_status_q || exit 7
        restart
            ;;
    *)
        echo $"Usage: $0 {start|stop|reload|configtest|status|force-reload|upgrade|restart|reopen_logs}"
        exit 2
esac