Ask someone else. Anyone you ask to write an LOR is free to decide whether or not to do it for any reason of their choosing or even for no reason at all. But if they don't want to do it, somehow pressuring them into doing it anyway is unlikely to result in a really positive letter that's going to be of any help. Asking someone to write an LOR for you is pretty quick way to find out what someone thinks of you. If they decline, you got your answer and you need to move on.
Realistically, not all that many people get along all that great with their supervisors or want to share their plans with them, especially if that's why they're leaving. (In industry, the popular adage is that no one leaves a bad job, they leave a bad manager.) It's a common experience everyone has sooner or later, so it's unlikely anyone will ever think it's odd if your LORs come from other people.
Unless the person writing your LOR is exceptionally well-known, it's usually far more important what the letter says, e.g., the nature and detail in the observations being reported in support of the recommendation, than who signed it. Best to find people who are unreserved in their willingness to help you -- then help them with whatever info they might find helpful, e.g., your transcripts, CV, any essays you'll submit, etc., so they can write a really good letter.