We've been to Tenerife for the last 5 Xmases (and hopefully this year as well). South Tenerife is usually better, as the north is generally cloudier. We usually stop in Playa de Las Americas/Costa Adeje.
December is, on average, the wettest month in Tenerife (followed closely by November, then January), but in all the times we've been, it's usually been nice. If I remember correctly, we had rain for 2 or 3 days on one holiday, then it was nice again - usually long sunny spells with some cloud cover on some days.
During the day it's shorts weather and sunbathing is quite pleasant. At night time, I was quite comfortable wearing a t shirt and jeans.
Average weather for Tenerife:
http://www.holiday-weather.com/tenerife/averages/