1. Double check SPIRE, make sure there isn't a hidden second, third, or even fourth lecture buried in the list, scroll down the list slowly and expand it if necessary.
2. Determine why it is you need the class, if there is a really good academic reason for you to take that class, e.g. it satisfies a prerequisite for application to a closed major or to an upper level course you need to take in an entirely different major, a professor might be more open to the idea of allowing you an override into the course. Once you've made that determination head over to the professor's office during posted office hours; you could also try emailing, but a face to face interaction will be in your best interests.
3. Consider waiting till summer and check to see if the university is offering the course through continuing education. You could also try taking a class closer to home at another school, but always consult with your academic advisor before making either of these decisions, as there are other considerations that have to be made before taking either a summer or transfer course elsewhere; you wouldn't want to accidentally take a course that you won't get credit for here at UMass!
4. Wait it out and keep a regular eye on SPIRE. Sometimes, a seat or two will open up sporadically between the time you register and the start of the next semester and a lot can happen between now and then. So, even if a class is closed, keep it in your shopping cart and if the status goes form Red to Green, you will be able to quickly add it. Occasionally, departments might even add an extra section of a popular class, particularly if there is high demand. Also, a lot of courses have a wait-list option, add yourself to it if possible, because at the start of every semester there is typically a large drop-rate form courses for a variety of reasons, this is a great time to get into a closed class.
5. Finally, if all of the above fail, just try showing up to the first day for that class you really want to get into, you might just get an override from the professor, particularly if there are a lot of empty seats in the auditorium that day. Remember, don't be afraid to speak with the professor, you are your best advocate, so get out there and get that class!