Henry Jenkins uses several examples of converging media - broadcast and grassroots with Burt and Osama; voice, film and text with cell phones; games, film, communication with consoles - but some rebuffing of this convergence is significant.
Jenkins says he was "told by company after mobile company that they don't make single-function phones anymore. Nobody wants them;" I would argue plenty of people do - Jenkins did, I did last time I looked for a phone - but cell phone companies can't make any margin in the highly commoditized cell phone market unless they throw plenty of features into the device whether they make sense or not. Of course a cell phone is an example of technological convergence and Jenkins' primary argument was about increasing cultural convergence... Is talking to the same person via email, cell phone, instant message, and xbox live a cultural convergence even though they are performed on separate technologies?
The quote Jenkins uses from /i/Technologies of Freedom/i/ - "A single physical means [...] may carry services that in the past were provided in separate ways. Conversely, a service that was provided in the past by any one medium [...] can now be provided in several different physical ways. So the one-to-one relationship that used to exist between a medium and its use is eroding." - implies that yes, the use of separate technologies for the same service is convergent.
The use of separate technologies in this culturally convergent way supports Jenkins' claim that "convergence is a process, not an endpoint. There will be no single black box that controls the flow of media into our homes," because the differing interfaces of different technologies call for use in different contexts and one can't fully replace the other even if their uses overlap. One can make a phone call through their cell phone or computer, but the portability and flexibility of the phone makes it better suited most of the time - equally one can watch a movie on their cell phone or computer, but the screen size, capacity, and broadband connectivity of the computer make it better suited. Technologically divergent by application, culturally convergent by use.