server {
  listen 81;
  server_name localhost;

  access_log off;
  allow 127.0.0.1;
  deny all;

  location /nginx_status {
    # Choose your status module

    # freely available with open source NGINX
    stub_status;

    # for open source NGINX < version 1.7.5
    # stub_status on;

    # available only with NGINX Plus
    # status;

    # ensures the version information can be retrieved
    server_tokens on;
  }
}

server {
  listen 8080;
  location /api {
    api write=on;
  }
}

server {
  listen 80;
  status_zone <ZONE_NAME>;
  ...
}

sudo nginx -t && sudo nginx -s reload

kind: ConfigMap
metadata:
  name: nginx-conf
data:
[...]
  status.conf: |
    server {
      listen 81;

      location /nginx_status {
        stub_status on;
      }

      location / {
        return 404;
      }
    }    

spec:
  containers:
    - name: nginx
      ports:
        - containerPort: 81
      volumeMounts:
        - mountPath: /etc/nginx/conf.d/status.conf
          subPath: status.conf
          readOnly: true
          name: "config"
  volumes:
    - name: "config"
      configMap:
          name: "nginx-conf"

http {
    #recommended log format
    log_format nginx '\$remote_addr - \$remote_user [\$time_local] '
                  '"\$request" \$status \$body_bytes_sent \$request_time '
                  '"\$http_referer" "\$http_user_agent"';

    access_log /var/log/nginx/access.log;
}

LABEL "com.datadoghq.ad.check_names"='["nginx"]'
LABEL "com.datadoghq.ad.init_configs"='[{}]'
LABEL "com.datadoghq.ad.instances"='[{"nginx_status_url": "http://%%host%%:81/nginx_status/"}]'

LABEL "com.datadoghq.ad.logs"='[{"source":"nginx","service":"nginx"}]'

apiVersion: v1
kind: Pod
metadata:
  name: nginx
  annotations:
    ad.datadoghq.com/nginx.check_names: '["nginx"]'
    ad.datadoghq.com/nginx.init_configs: '[{}]'
    ad.datadoghq.com/nginx.instances: |
      [
        {
          "nginx_status_url":"http://%%host%%:81/nginx_status/"
        }
      ]      
  labels:
    name: nginx

apiVersion: v1
kind: Pod
metadata:
  name: nginx
  annotations:
    ad.datadoghq.com/nginx.checks: |
      {
        "nginx": {
          "init_config": {},
          "instances": [
            {
              "nginx_status_url":"http://%%host%%:81/nginx_status/"
            }
          ]
        }
      }      
  labels:
    name: nginx

apiVersion: v1
kind: Pod
metadata:
  name: nginx
  annotations:
    ad.datadoghq.com/nginx.logs: '[{"source":"nginx","service":"nginx"}]'
  labels:
    name: nginx

{
  "containerDefinitions": [{
    "name": "nginx",
    "image": "nginx:latest",
    "dockerLabels": {
      "com.datadoghq.ad.check_names": "[\"nginx\"]",
      "com.datadoghq.ad.init_configs": "[{}]",
      "com.datadoghq.ad.instances": "[{\"nginx_status_url\":\"http://%%host%%:81/nginx_status/\"}]"
    }
  }]
}

{
  "containerDefinitions": [{
    "name": "nginx",
    "image": "nginx:latest",
    "dockerLabels": {
      "com.datadoghq.ad.logs": "[{\"source\":\"nginx\",\"service\":\"nginx\"}]"
    }
  }]
}