That's not so easy to answer as you might think. It depends whether the data you're seeing is coming from an organic search engine listing, a directory, a PPC or a paid inclusion listing.
There are no search engines that state precisely their update information for the organic listings. Many services will take months to update their index, if at all. ;)
With regard to directories, that is really down to each individual directory and to their review proceedures.
The only way to get results in the two-day time frame you mention is with a paid inclusion or PPC listing. Potentially, that would be only a day or so - allow 48 hours.