AppDatePicker.vue

<template>
  <div>
    <date-picker v-model="date" />
  </div>
</template>

<script>
export default {
  data() {
    return {
      date: new Date(),
    };
  },
};
</script>

nuxt.config.js

  plugins: ["~/plugins/datepicker.client.js"],

plugins>datepicker.client.js

import Vue from "vue";
import DatePicker from "vue2-datepicker";
import "vue2-datepicker/index.css";

Vue.component("date-picker", DatePicker);