Cron job would be appropriate to use. Here's an example of 3 nginx pods accepting all traffic, every minute, a Job curls 1 of the 3 pods (always the same pod).
apiVersion: apps/v1beta1
kind: Deployment
metadata:
  name: main
  labels:
    app: nginx
spec:
  replicas: 2
  selector:
    matchLabels:
      app: nginx
  template:
    metadata:
      labels:
        app: nginx
    spec:
      containers:
      - name: nginx
        image: nginx:1.7.9
        ports:
        - containerPort: 80
---
apiVersion: apps/v1beta1
kind: Deployment
metadata:
  name: singleton
  labels:
    app: nginx
    special: singleton
spec:
  replicas: 1
  selector:
    matchLabels:
      app: nginx
      special: singleton
  template:
    metadata:
      labels:
        app: nginx
        special: singleton
    spec:
      containers:
      - name: nginx
        image: nginx:1.7.9
        ports:
        - containerPort: 80
---
kind: Service
apiVersion: v1
metadata:
  name: allpods
spec:
  selector:
    app: nginx
  ports:
  - protocol: TCP
    port: 80
    targetPort: 80
---