My New Year's resolution for this class is...After giving them a chance to think and write, discuss their resolutions as a whole group. You might want to talk about why people make New Year's resolutions, perhaps giving them a bit of history to explain the tradition. Let your students define "outside of this class" however they like.
My New Year's resolution for outside of this class is..
Also, you must, must, must share your resolutions, and as always I'd advise you to be frank and honest about what didn't go well in the fall that you want to fix. Your "outside" resolution is a chance to let your kids get to know you a little better as well.
This is essentially a chance for reflection on the fall semester and a goal-setting exercise for the rest of the year, which is a cycle that you should be following when it seems like your students aren't buying in to what you're doing. It's also an example of taking advantage of things going on in the real world to create a context that engages and invests your kids.
One thing I didn't do that I would recommend is to have your students write these on a notecard or something else you can easily collect and save. Then you can share them with your students at the end of the school year to see if they followed through (because as you know, everyone sticks to their resolutions).
Just remember, this is a time-sensitive activity. If your new semester has already started, use it tomorrow or Monday. If you start next week, you only have that first week to do it before it will lose it's relevance.