Try this

OK, here’s the deal. 

Put a pile of rocks at the bottom of the Washington Monument. Drop a super ball from the top of the Monument onto the rock pile. Make it stick--without bouncing. 

This is like dropping a probe onto 67P/Churyumov-Gerasimenko, with gravity “several hundred thousand times weaker than that on Earth”, and making it stick.

Winner reports immediately to the European Space Agency.

Personally, I like the idea of a net of some sort that would be deployed upon contact. Hopefully, it would snag and grab on to something... The key here is slowing the probe down as much as possible before it makes contact. Since gravity is so weak, I look at this more like docking one spacecraft to another in space. It seems to me that the "mother ship" could get pretty close, in distance and in speed, to the comet before the probe is released. Placing the probe on the comet's surface would be better than it hitting the surface at a relatively high speed.

I also see a problem with orienting the probe properly--top is up; bottom is down. It seems to me that this is another step after the probe has landed (and stopped bouncing). The first thing that occurs to me is to try to design the probe without a top or bottom--so that it would operate however it was oriented when it settled down. If that isn't possible, then perhaps a series of small motors could be used to orient it and to level and plumb it correctly, e.g. making it "right-side-up" if it lands "upside-down".

My hat's off to the ESA. They've accomplished a remarkable feat just getting to the speeding comet, much less landing a probe on it. 

ABSOLUTELY AMAZING!!!