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I can use MyEtherWallet to generate a new Ethereum address. But using it I generate one address at a time. This takes a long time to generate, let's say, 100 private keys.

Is there a way to automate this process?

For example, I click one button and 100 (or any number) Ethereum private keys are generated.

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If you are talking about programmatically, yes of course! Ethereum web3js allows you to generate public addresses with a private key generated programatically. Calling that function allows you to generate as many keypairs as you wish in short amount of time dependant on performance.

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Get web3

var Web3 = require('web3');
var web3 = new Web3('ws://localhost:8546');
var accounts = web3.eth.accounts;

var keys = [];
var amount = 10;

for(var i = 0; i < amount; i++) {
    keys.push(accounts.create(web3.utils.randomHex(32)));
}

This should in theory do it.

Docs

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