No account at Coinbase or any other online exchange is required to own bitcoin. In fact, to have someone else hold your money is against the spirit of Bitcoin.
Everyone is their own bank. All you need is a Bitcoin wallet and I recommend exactly that app, Bitcoin Wallet: https://play.google.com/store/apps/details?id=de.schildbach....
There are many others as well. BitPay has a user-friendly one called Copay: https://play.google.com/store/apps/details?id=com.bitpay.cop...