There are a lot of resources for problem solving online.
One place to look is MIT's OpenCourseware; see their Problem Solving Seminar:
This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.
You might also be interested in some of the Art of Problem Solving (AoPS) resources. The site also has recommended books for a variety of mathematics contests; see here.
Ideally you would find someone with experience doing MathCounts, IMOs, or (since you are in the Boston area) PROMYS. You might look specifically into contacting the people with PROMYS for Teachers.
If none of your prospective participants has experience with problem solving competitions: I will second Dave L Renfro's comment about focusing on the first couple of problems in each session, i.e., A1, A2, B1, and B2. It is quite possible for a mathematics major who has no experience with these competitions to rack up points on these problems: usually the scoring would be 1 (something of relevance), 2 (partial solution), 9 (almost a full solution), or 10 (a full solution). With a fair bit of practice, first time test takers should be expected to score a 10 or 11 on the examination (and, as you said, even scoring a single point can be enough to surpass the median).
A word of caution: More than helping students to do well, I would emphasize that a poor performance on the Putnam does not entail an inability to do mathematics (or even be a professional mathematician). Like all things, doing well requires practice, and students who have not competed in MathCounts, IMOs, etc in the past are unlikely to score very high in this competition. Moreover, you write:
Keep in mind that these students might not be willing to put in that much extra time outside of coursework.
If the students are unwilling to put in a lot of time and are not experienced in this type of problem solving, then they may well be shut out.
Final suggestions: Free food is one way to entice students. Another method is to see if some sort of prize (even if it is just a certificate) can be awarded to the student who scores the highest at your institution on the Putnam. Note that the highest scorer might not be a mathematics major: See if those with other majors - e.g., Computer Science, Economics, Physics - have any interest in participating (especially with the free food). Separately, I know of at least one other small, MA liberal arts college that offers its own internal problem solving award: see more on Amherst College's Walker Prize Examination here and links (without solutions) to tests from 2009-2012 and 2013.
And if you do manage to get (non-graduating) students interested enough to take it: Try and see if they will help out with the preparations the next year. Doing well on this competition and maintaining student interest are both matters of school culture in addition to some raw talent and a lot of practice.