As others pointed out, Amex is the only option for no annual fee. But I have an idea for you to consider.

For now, save the MRs with an Everyday card. But since you're not going to be too lucky finding multiple seats with miles on a particular flight (as was pointed out by Aristophanes80), down the line you sign up for an Amex Platinum card. Yes, it has a $550 annual fee but it comes with access to the "International Airline Program". The quotes I've received with them are ~15% off business class tickets. That's more than $550 savings on a single return business class ticket, plus 5x points, plus you earn miles on a revenue fare. If you do that for one or two, and use miles for the rest, then you're in business