Hopefully someone who knows can give careers advice for master in psychology. But learning to program, even just the basics, will be beneficial to you whether or not you make a career of it.

Check how much you can make. Apply for jobs, interview and see what kind of offers you can get. It's not completely worthless, at worst it signals intelligence and conscientiousness even if you never apply anything you learned, ever. With a soft degree having good stories about how you're awesome/capable is more important than proving you can do something in the interview.

Study CS and programming if you find them interesting. The monetary cost isn't very high and if you enjoy it you can become good at it, and that is worth real money. Try it. Even being competent at SQL is (so I am told) quite employable though getting an entry level job without a qualification would demand a lot of perseverance. SQL zoo is apparently a good site for learning it. If you want to learn a programming language Python is often recommended as a beginner language. If you want a text that assumes no previous knowledge Learn Python the Hard Way is the source to consult.

The common advice I've seen is to spend a few months contributing to some open source project. See this blog post, for example. (The advice in that post is hard to follow unless you already know C++ and feel like banging your head against the enormously complex Google Chrome codebase).

I'm also trying to get a programming job, but my hangup so far has been finding an open source project that I find interesting enough to contribute code to.

I disagree, middling programmers make great livings compared to middling or even above average people in many many fields.

Agreed with nazgulnarsil. I'm a competent-at-best coder, and only work as a test engineer, I've got no formal qualifications in the field, and I've only been working as a software engineer two years. Yet I earn more on my own than the average household's income in the UK, my work is often interesting, I have more flexibility about things like dress codes and working hours than in any other job I've worked, and I get on with my co-workers.

Math is not necessary for many kinds of programming. Yeah, some algorithms make occasional use of graph theory, and there certainly are areas of programming that are math-heavy (3d graphics, perhaps? Also, stuff like Google's PageRank algorithm uses linear algebra), but there are huge swaths of software development for which no (or little) math is needed. In fact, just to hammer on this point, I distinctly remember sitting in a senior-level math course and overhearing some math majors discuss how they once took an introductory programming course and found the experience confusing and unenjoyable. So yes, math and programming are quite distinct.

The probability I would place on you being able to make a living doing programming is dependent on only one factor: your willingness to spend your free time writing code. There's plenty of people with CS degrees who don't know how to program (and, amazingly, don't even know how to FizzBuzz), and it's almost certainly because they've never spent significant amounts of time actually building software. Programming is "how-to" knowledge, so if you can find a project that motivates you enough to gain significant experience, you should be set.

I'd guess most people fitting that description won't make a living as programmers, but the good news is, you don't have to guess in advance. Just try it and see if you get in to it. You're very unlikely to regret it whether it turns into a living or not.

No direct experience here -- I got my current job a year or so before the recession hit -- but secondhand accounts suggest that the demand for programming jobs right now is highly regional. Here in the SF Bay Area the job market seems weak but basically stable, but I have friends on the East Coast that claim their respective companies have been forced to hire substandard applicants just to put enough bodies in chairs.

Here in London my programmer friends don't seem to be having trouble staying in work, while my employers are pretty much always recruiting.

Speaking as an undergraduate student in a computer science department, I can confirm your observation. I have also observed that while coding, the philosophical pumps start working and good -- or at least interesting -- ideas about other subjects are often produced. The most interesting off-topic conversations I have had with other students in any class have been had in computer science classes.

I have also noticed that my ability to deal with mathematical problems that are generally algorithmic mentally has been improving rapidly. I suspect the regular practice of holding a process in one's mind while encoding it is related to this.