Nope, I once posted a thread about clearing the airline's cookies to get an honest search, but that trick was short lived. Now they have programs that ID your computer with a high degree of accuracy by reading other info from your computer, i.e. your ISP, browser, extensions, etc.
Now there is a wide variety in fares for different days, but you can get honest searches at Kayak.com, Orbitz if you're not looking for American tickets, other searching sites. Just not from the airline's site.
If you want to, call Continental and ask for the Continental.com Help Desk. That might work better, but - why bother?
It's not like they have 6 other airlines competing for your business anymore.
Have your tried searching on Kayak? I have Sidestep.com bookmarked from years ago, altho they are now the same thing, so my examples may look a little different from what you will see but this is my initial approach. Click pics to enlarge...
To search March 1-14 possibilities, I select 3 & 11 with
+3 days, and select 6am departure for first preference...

This gives me the lowest fares for 7 different departure days and 7 return days, with combinations....

The lowest fares will be illustrated below.
Then I uncheck overnight itineraries to avoid those as I examine more closely. That 6am flight may not go every day, but it does fly some days in March for sure...

Then I Change Search, check nearby destination airports, and take a look at flying to/from Cancun...

To is not so bad as from, but you can also play with Open-Jaw booking into Cancun, return from Coz.