Do you have a weekly rate to my destination?

No. You can schedule but no weekly rate.

Since rideshare services like Uber and Lyft are "on-demand" services, they are meant to be requested at the time of the ride, and hence it is not common for one to "schedule" multiple scheduled trips.  (That does not mean you cannot schedule them in advance.  Here's an article on how.)

So on that note, no, there does not seem to be major rideshare services that offer weekly discounted rates. (At the time of this writing - 2017/02)  

Lastly, Uber is indeed starting to create arrangements with corporate customers.  Perhaps this can lead to volume discounts.  We will see!

UPDATE (2018-02): 

Here's a relevant article you may find useful.

How to Save Money Using Uber & Lyft: Frequent Rider Programs and Commuter Passes

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC