I'm retired now but I bluffed my way into several courses - including a Masters. Luckily I went on to get the qualifications.
If you got a first-class degree in anything, (apart perhaps from a so-called "soft" subject, I won't go into details), then this in itself is enough to indicate that that you are bright enough and determined enough to cope with studying at Masters level (IMHO).
My suggestion is that you pick one of these profs who know you the most and try an experiment.
Write your own reference, laying out your strengths, e.g. Works hard, capable of team work, but also capable of working alone, excellent attention to detail in the lab, etc, etc. Make sure that you are truthful and realistic.
Now comes the experiment (let's face it you have nothing to lose)
Send the above reference to one of the profs who has refused. Ask if s/he would be willing to send it as one of your recommendations even though it says nothing about computing skills. Ask them simply to redact or amend anything that is not true. This will save them a lot of work.
The professor can respond in a number of ways. Let's consider two.
They give you a straight "No". Then you are no worse off because they weren't going to anyway.
They say "Yes", then you have the opportunity to go ahead. Make sure you do use the letter though or the prof will resent putting in even putting in the limited amount of work.
There are Masters and Masters. Some are clearly designated as conversion courses. They are for experts in other fields who want to add new knowledge; These courses are rather like doing a three-year first degree but in one year. This is tough but can be done - however you won't get too advanced - probably you'll only be able to reach graduate level in the subject.
Others are intended as an advance from a first degree in the same subject. In my opinion, unless you are a genius) you would be crazy to attempt this coming from a different subject. Computer science is not about having written a few C programs or any other programming language. It is about understanding data structures (trees, stack, heap etc), search algorithms, graph traversal, computability theory, operating systems, machine architecture, etc. (Those are just the first that came to mind). Already being fluent in several different programming paradigms (OOP, Functional, Procedural, etc.) is taken for granted.
I think you should carefully read the prerequisites for the course and see if you believe you have them. Otherwise think again.