Welcome to TF!
I assume you mean for the winch or hoist motor on the davit. Is that correct? If so, a davit's hoist motor is often made by someone other than the davit manufacturer or has been replaced since the davit was installed. Can you see a manufacturer's name and model number on the hoist motor? Do you have a remote and are looking for a replacement? Is it a wired remote? Oops, you said 'transmitter,' so it's probably not wired. Can you post pictures of what you do have, including the remote interface at the davit and the controller?
So many questions, and I have others, but if you fill in some of the blanks, we'll be able to ask more useful ones.