from Morznet;
For summer 2009, the lifts will be open in Morzine & Les Gets from 19th June until 6th September inclusive and the entirety of the Portes du Soleil area will open up on 26th June until 30th August. However, this year, Les Gets will be opening some of it's lifts earlier than normal so that you can get in a bit of weekend biking before the main season begins. The Chavannes chairlift and the Mont Chery gondola will be open from 30th May to 19th June, weekends only, and there is also the possibility of extending the opening dates of these lifts until 13th September, weather permitting.
it does vary from year to year, especially in newer resorts (meaning ones that only started opening for moutainbikers recently) but Morzine is pretty established so I expect those dayes will be similar for '10
May have a look at Zermatt in September Trailseeker, sounds fun, great reputation and I've never been there!