How can I have my father in law, who is bedridden due to his illness, transported to GA from NY?

I would not move him. From my home in SNJ to Marietta, GA its a 12 hour drive we do in two days. I, also think that it would be better to go there.

If your FIL is on Hospice there is a slight possibility that Hospice can arrange something like this. Most Hospice have a "Foundation or Charitable" arm and can they have been known to pull off some amazing things.
Renting an RV or accessible van might work as long as he does not need medical treatment/care during the transport. Do know that any transport will take a toll on him and may hasten a decline. Travel for anyone is stressful.

As I mentioned above Hospice can be very helpful and there is also the other option of your husband traveling to his dad rather than moving dad. And Hospice may be able to help with that if your husband needs help in that aspect.

I have read of people who rented an RV for transport, that would take a little logistical planning and only you know if his condition would allow that.

If he is that sick there are no other real options than transport by ambulance, which is expensive. It may be less expensive for someone to go and stay with him in NY until he passes. Just a thought. I'm sorry that your family has to deal with situation.