Present a copy of your most recent tax return, if you filed during the past year and had no income. While last year's tax return doesn't prove the current year's income, it will prove you had no income last year and bolster your case that you've had no income since then.
Gather your bank statements for the previous three to six months (or more) to demonstrate that you've made no deposits in that time. Again, while this is not definitive proof that you've received no income, having made no deposits to your bank account does help to suggest that you've had nothing to deposit.
Visit the IRS website and download Form 4506-T, "Request for Transcript of Tax Return." Complete the form and return it to the address indicated, and you'll receive a list of all income sources from the previous year. You may also use it to request proof of any W-2s or 1099s issued under your Social Security number, and proof that you filed no tax return in the previous year. The form is free to file.