Sometimes it takes days, sometimes it takes weeks. Also, if the website that you used to sign up to CJ with is not in the same niche as the affiliate program that you're applying to, you will most likely get turned down. Personally, I like to find or get approved for the offer first and then build a site around it, but with CJ, you must already have a suitable site before you apply to any program that requires manual approval (that is, if you want to get approved).