If you can't find the payer's EIN (or FEIN) on the 1099-DIV, please give the payer a call to get it. The IRS will not allow you to e-file the form without that number.
Employer Identification Numbers are public information, so the payer should have no concerns about divulging that number to you.
If you are unable to get the number, type 99-9999999 in the software. You will have to mail your return to the IRS.