Why not check out the private rentals on the forum. Personally I wouldn't wait, accomodation for Christmas / New Year in Tenerife is always booked quite some time in advance. Come Easter you will probably find it very hard to get anything for Christmas/New Year

You could try 365sun-tenerife.com, found these to be a very helpful company,have booked accomadation for next xmas & new year with them

.....you could also try this company for a good choice of accomodation :http://www.tenerifetemptatons.com.....we have used them in the past, and have always received good service from them; Ann there is very helpful.
Good luck with your search...its never too early to book for New Year !

Just be careful who you book with we got let down badly last year and the company were not ABTA or ATOL bonded never again.

would echo the last reply We were very badly let down when
we booked for new year. We booked an apartment through soimeone advertising on holiday truths (Thought would be safe but we were wrong), the apt didn't exist and we were moved to different resort into bad accommodation whilst paying top price. All our friends were staying in area we booked and we were miles away!! Still battling for some compensation
So beware!!