Is it possible to watched my recorded programs on my iPad with Contour?

Currently this feature is not available.  I'll share your suggestion with our product team.

This is possible with a TiVo Roamio, you should check it out, this replaces your Cox equipment, instead you would rent a CableCARD and Tuning Adapter from Cox for $2/mo.  There are several plans and several Discount codes for discounted equipment and Lifetime Service.

4 Tuner - Base Roamio (TiVo Stream also needed for watching on iOS and Android)

6 Tuner - Roamio Plus and Pro the Streaming device is built into the DVR.