I can't tell you an exact number, but I found a more or less interesting site:
Especially the deep sea section should be what you're looking for. Especially this operator provides some deep sea tours. I couldn't find anything similar and haven't heard of it too.
When you read the description of this tour, it says that you can take some tours with a MIR submarine and it is possible that you can dive up to 6000 meters. There aren't a lot of places in the oceans that are deeper, so I can't imagine that as a tourist you will be able to find a tour that takes you any deeper.