To teach genre I was thinking about having an assignment with two parts: first the students would choose a genre that they are familiar with and write about the core rules and rhetorical strategies of the genre, and who the desired audience is. After they have solidified their set of rules, I would then have them analyze a work of art in the genre of their choosing through the rules that they have written.
The second part of the assignment would be for them to locate a parody of the genre they are choosing, and have them write about the parody and whether it adheres to or plays with the rules of the genre that they had established previously. After they have analyzed this, then they will be asked about the effects that the parody has on the desired audience.
I did something similar at the beginning of our multi-modal composition unit on the discussion board this semester after instruction began online and the students seemed to understand and respond well. Since this was successful I think it could be easily done through online platforms.