It depends on that kinds of changes you want to make to your live database.
In your question you only talk about adding new tables and stored procedures.
As long as you only add new stuff (tables, sprocs, or even new columns to existing tables) you don't have to do anything special, because SQL Server can do this while the database is in use and the changes don't affect your users because their version of your app doesn't even know about your newly added stuff.
On the other hand, it gets way more complicated if you change or even delete existing stuff.
There is a great chance that this will be a breaking change for your app, as it will probably stop working when tables look different than it expects or if it tries to access tables/sprocs that don't exist anymore.
(Even if you only add new stuff like I said in the beginning - you will probably want to update your app anyway, so it can actually USE the new stuff in the database)
So you probably will need to make your database changes AND deploy a new version of your app as well, both at the same time.
I'm no ASP.NET expert, but as far as I know it's not possible to update an ASP.NET app without all active users getting kicked out.
So in this case you would have to do what OMG Ponies already said: choose a time when the least possible number of users is affected, and/or inform your users early enough about the scheduled outage.