With most directories you will be lucky to get a link within a few day's, let alone a few hours. I know that is not the answer you were looking for, but truth be known I doubt their are many directories if any at all that will approve and put your site up within 2 hours.
good luck on finding such lists. directory owners have other things to do and most active directory owners usually approve once a day. some every few days depending on the submission volume. there are some that can take months.
the most faster its 24 hours for a paid submission make a post and ask people with web dirs to approve you now for a fee
whats the point in this question, even if anyone does activate your link in 2 hours (which absolutely nobody will!!) - it could take another 6-8 weeks for google to cache that link. also its polite to thank those that have responded with advice and not simply demand more pointless info!!
first of all, are you asking for a free directory sites?... some directories takes about almost a month or 2 before you see your submission listed on their site... then, good luck on finding such directories, (bravenet directories are like the one your asking for, but I don't think that you can get the most out of them).
why are you going for directory submission nowadays...it is worth less.....do Social Networking & Bookmarking that will be good.
Ya i agree that......it is better you can prefer doing Social Bookmarking rather than Directory Submission or else you can go for paid directory Submission sites!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
You may not be able to find such a link because even if you try the paid versions of the links on directories, in most cases it will take something like 12 or 24 hours before your links are displayed.
See at dp dir forum, min approval time is 12 hours. I don't know those websites its hard to find but u must submit website in dp members dir. they will give fast approval