See http://theglassicon.com/computing/web-servers/install-nginx-amazon-linux-ami

Amazon Linus AMI nginx

#!/bin/sh
### BEGIN INIT INFO
# Provides: nginx
# Required-Start: $local_fs $remote_fs
# Required-Stop: $local_fs $remote_fs
# Default-Start: 2 3 4 5
# Default-Stop: S 0 1 6
# Short-Description: nginx initscript
# Description: nginx
### END INIT INFO
#
# processname: nginx
# config:      /usr/local/nginx/conf/nginx.conf
# pidfile:     /usr/local/nginx/logs/nginx.pid
 
# 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="/usr/local/sbin/nginx"
prog=$(basename $nginx)
 
NGINX_CONF_FILE="/usr/local/nginx/conf/nginx.conf"
 
lockfile=/var/lock/subsys/nginx
 
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 $prog -QUIT
    retval=$?
    echo
    [ $retval -eq 0 ] && rm -f $lockfile
    return $retval
}
 
restart() {
    configtest || return $?
    stop
    start
}
 
reload() {
    configtest || return $?
    echo -n $"Reloading $prog: "
    killproc $nginx -HUP
    RETVAL=$?
    echo
}
 
force_reload() {
    restart
}
 
configtest() {
  $nginx -t -c $NGINX_CONF_FILE
}
 
rh_status() {
    status $prog
}
 
rh_status_q() {
    rh_status >/dev/null 2>&1
}
 
case "$1" in
    start)
        rh_status_q && exit 0
        $1
        ;;
    stop)
        rh_status_q || exit 0
        $1
        ;;
    restart|configtest)
        $1
        ;;
    reload)
        rh_status_q || exit 7
        $1
        ;;
    force-reload)
        force_reload
        ;;
    status)
        rh_status
        ;;
    condrestart|try-restart)
        rh_status_q || exit 0
            ;;
    *)
        echo $"Usage: $0 {start|stop|status|restart|condrestart|try-restart|reload|force-reload|configtest}"
        exit 2
esac

Run with sudo service nginx {start|stop|status|restart|condrestart|try-restart|reload|force-reload|configtest}