How would you get your stimulus check if you only have a checking account?

an ordinary check will be mailed to you.

If you have not provide direct deposit information to the IRS or the Social Security Administration, then the check will be printed on paper, placed in an enveloped, and sent to you by U.S. mail. It may take a few months to print all of them.

The stimulus check will be sent to you by postal mail.  

Get My Payment portal at IRS.GOV (new today) let's you enter direct deposit information.  Have your checkbook handy as well as your 2019 tax return.

It would come by regular mail as a paper check.

Expect to get it in the mail in a few weeks

if your income tax was sent direct deposit to your checking account then that is the way they will send the money--if not it will come to you as a check.