Since you won't say why you want to do this, I must assume you are running a cloud service that has reached its capacity. Congratulations on your newfound popularity!
While you work on improving your backend, I recommend that you write some logic into your app that will show the user a friendly specialized screen whenever your servers are at- or over-capacity, letting them know that they did nothing wrong and your service will be back soon. This way, they already have the app installed and can instantly start using it when you eventually get the problem solved.
This is better than saying "Sold Out" or "Out of Stock" on the App Store page. What does that imply? Does it mean that there was only ever a limited number, so no one else will ever get any? Does it mean the potential user should check back later? What if they forget to check back once you're back up and running?