The only thing which comes to my mind is to look for BnB and then negotiate a price because you take it for a month or several. That's what we were doing a year a go. For example in Aubonne there was a small 30 sq m studio for exactly 800 CHF per month. Now you have chances because it's winter and for La Cote the hot season is summer. So search on
http://bnb.ch
And I would not try to find only in the villages which are main train stations like Morges or Lausanne. In places like St George or Savigny there are more chances.
PM me if you have another questions.
P.S. Actually the search on homegate.ch also gives its results so you should try there. But it works only if you rent for at least 1 year. Though on bnb.ch you can get an apt for a month or two.