Do caribbean medical schools accept students with average grades?

I think they accept just about anyone.  After you get your degree you can work for my HMO.

I think you should do some research on the web. I found, for example, that the Saint James School of Medicine, in Bonaire, takes applicants with a minimum 3.0 GPA, and that they need to have taken the MCAT. I didn't study in the US, so I'm not familiar with the GPA system, hence, I don't know if that's average.
I think that if you're serious about school, it's not about going to a a place that takes anyone. If the school is not accredited, your diploma is worthless. Also, schools that take just anyone will leave you with a shitty diploma and, since it's the Caribbean, a sun tan.