According to a report on industry blog Gamasutra, the PlayStation Store will be returning in less than a week. Gamasutra's source is a memo sent to developer that says, barring any further problems, the Store will be back up on May 24, which would mean PSN users should get to claim their "make-good" gifts from Sony before June
According to the memo, the Store will be publishing two updates per week in order to catch up with the PSN downtime schedule.
When the PlayStation Store reopens, it will distribute content that was originally scheduled to publish on April 26. Then, three days later, the next set of games and demos will go up. Content will drop on May 31 and June 3 that was originally planned to be spread over three weeks. After that, the company will be back on its regular weekly schedule.
Joystiq also has a similar article saying that it will be up by Tuesday. Here is a link
As someone who has missed out on Honest Hearts because of the outage I can only say the sooner this happens the better.
UPDATE: Sony is giving PlayStation 3 users one month free of Playstation plus as well as the choice of two of the following titles, available for 30 days shortly after PlayStation Store is restored. They can be kept forever:
Super Stardust HD
Wipeout HD + Fury