As this article says wish can be used in informal speech in the continuous tense, which was done in the 15th episode of the 5th season of the TV show Friends. Here is the excerpt:
Monica: (kneels with him) Chandler, umm, I want you to take just a minute and I want you to think about how ridiculous this sounds.
Chandler: Yeah, I'm kinda wishing everyone wasn't here right now.
How would the meaning of the sentence change if Chandler said I wish instead of I am wishing?
The meaning would not change in the particular situation. Chandler could equally properly say 'I wish' or "I'm wishing' that 'everybody isn't here'. We can use the present continuous about something which is happening in the present ("right now") if we wish to emphasise that it is happening at the present time. We would use the simple present 'I wish' to talk about a general wish that is not confined to the present, e.g. I wish people would drive more carefully.
The present continuous is used:
to describe an action that is going on at this moment: You are using the Internet. You are studying English grammar.
