The only place to get a Verification of Non-filing Letter is from the IRS. If you are unable to get it online, you can have it mailed to you, but it will take 5 to 10 days to get it.
Go to Get Transcript on the IRS web site, and scroll down to "Alternative to Requesting a Transcript Online." You can submit the request online by clicking the button that says "Get Transcript by Mail," or you can call 800-908-9946 to submit the request by phone. You can also request it by filling out Form 4506-T and mailing it to the IRS, but that will take longer.