Yes! Ownership and management of rental property is definitely a business! Go for it!
ETA: I believe it was
@CyndiLouWho who has the rental business.
If you're under 5/24, go for the CIP -- it's got a big UR signup bonus! You can also add Amex business cards to the mix since data points say Amex doesn't report business cards to your personal credit report so they shouldn't add to your 5/24. Amex is supposed to be among the most lenient about who they approve for a business card. However, keep in mind that Amex usually has once in a lifetime language attached to their signup bonuses, so you'll want to not waste an opportunity and be sure you are getting the highest or close to the highest offer when applying.
Anyway, a number of us have applied and been approved for the CIP, so if you have any questions feel free to ask!