If you have not paid the incentive yet, give the tenant a form W-9, which is a request for them to provide you with their tax number) and withhold the payment until they give you the number.
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/uac/about-form-w9">https://www.irs.gov/uac/about-form-w9</a>
If you already paid, or if they refuse to give the form and you really want them out, and you can't get the number, you can try submitting the 1099-MISC with a blank tax number. Maybe try writing "refused". You might have to mail in an old-school multi-part 1099-MISC on paper rather than submitting it electronically. (You can get the old style forms from the IRS for free.) You might need to give the IRS a written statement explaining that the tenant t refused and give as much info about them as you can (name, old and new address, birth data if you know it. etc.)
(Depending on how you run your rental operation, you really should have the SSN of every tenant. #1 so you can run credit checks before you rent to them and #2 in case you need to issue a 1099-INT for interest earned on the escrow account that holds their security deposit.)