There is no equivalent to the AddLayer, MoveLayer, InsertLayer functions that apply to table views. But from version 10.3, reordering layers/table views so that you can access them in a service won't be necessary anymore, since you are able to assign them an immutable ID.
Extract from this What's new in 10.3 document:
In ArcGIS 10.2.2 for Server and earlier, the layer and table IDs of a
map and feature services were not preserved after altering the source
map document. This required you to update any client applications
consuming the service to use the updated layer and table IDs.
In ArcGIS 10.3 for Server, you can now preserve the IDs of layers and
tables in map and feature services. When you create or alter a map
document, an option is now available that automatically generates
immutable IDs for each layer and table in the map document. If you
select this option, the layer and table IDs are preserved after
publishing or republishing; you are no longer required to alter client
applications that consume the map service. If desired, you can replace
the auto-generated IDs with your own custom IDs.
ArcGIS 10.3 will normally be released the week of December 9, and it's already available as prerelease for customers with a valid maintenance contract.