The latest offer for the Delta American Express with 10,000 bonus miles up front and the fee waived the first year is available, but only through August 31 (via Free Frequent Flyer Miles). The small business card is also available free the first year with 10,000 miles at signup. Yes, you can get both cards. And yes just about anyone qualifies as having a business (“Your Name & Associates”).
These are great ways to top off a Delta frequent flyer account. Be aware though that if you’ve received signup miles for a Delta American Express in the past that you’re unlikely to receive the miles again, at least for the personal card and likely for the business card. While many other cards (such as those issued by BankOne and Citibank) will allow you to claim signup bonus miles more than once, American Express generally will not.
Note also that after the first year each card charges an $85 fee, so you may or may not wish to keep them past twelve months.