Is there a reason you want to get the private key of your change address?
If its just to back your coins up, you just need the seed phrase which you got from blockchain.info when setting up the wallet.
To get the private key you can use
https://iancoleman.io/bip39/, like TryNinja mentioned.
But i would suggest you switch over to a wallet which lets you (and only you) have the control over your funds.
You always need to remember that blockchain.info (just a company - has nothing to do with the 'blockchain') has full access to your private keys.You have to keep in mind that you are relying on blockhain.info (as a company) to access your funds. This envolves trust at a point where you could easily rely on yourself instead of a 3rd party. [Edited for clarity]
Web wallets have a lot of additional attack vectors which 'standard' wallets (desktop-/mobile/hardware) don't have.
So unless there is a good reason for you to use a web wallet, a 'standard' wallet would be the safer option to store your coins.