Plate Tectonics: Is it possible to have an ocean-continent divergent boundary
The oceanic plates are themselves formed from the divergent boundary, so probably not. Even if a new rifting occurred exactly at the boundary, the result would eventually be that the ocean floor surrounds the divergent boundary. 

A very simplified model of an ocean would have a divergent boundary in the middle. This oceanic spreading center might have basaltic volcanic islands along it, and two mirrored plates on each sides, pushing towards neighboring continental or oceanic plates. 



I'm trying to think about any oddity that would fit your description, but can't really come up with a good example. Locally you might have the conditions in triple junctions eg. at Afar Triangle. Somehow, it could also describe parts of New Zealand and eastern Mediterranean, but it's very complex areas with more parameters controlling the rifting. 

Earth is not controlled by any simple equation, its formed by 4.56 billion years of interaction between rocks, magma, life, atmosphere and even astronomic influence, so I'm not sure that divergent boundary never occurred between existing continental and oceanic plates, but at least it's very uncommon and couldn't last long. 

A way to understand plate tectonics better, and maybe even a good inspiration for world building games, is to have a look at the (free) program Gplates that is used by students and scientists to simulate tectonic history. Don't worry about your ignorance, interest is more important than knowledge. The game might be a good inspiration for someone to learn more about something really awesome.