There is a very nice solution to generating random numbers from the Generalized Distribution of the second kind which can be found here.
There is a more general form of this which was developed by McDonald et. al. I have provided the link to my other question pertaining to this distribution where you can find further details as well as the functional form.
Is there a way to incorporate the parameter $c$ into the solution found in the aforementioned solution? I expect there to be a further transformation which would allow this but I have not made any progress on this front. I am curious to see if the community can assist.