Is it possible to customize the automatic date ranges in Advanced Search?
I'm not sure where to start as I can't answer the main question apart from quoting a colleague Jon Goldberg 29/Mar/15 5:19 AM 


  for now, you can use the PHP overrides folder to maintain your own
  local copy of this file when 4.6 comes out. I do this frequently for
  issues like this where I expect the problem to go away in the next
  version. I may do a diff if there's a security release of 4.6 that
  comes out that might change that file, but otherwise I leave things
  be.


This may or may not appropriate for your circumstances.

Personally, I would be reluctant to use "Upcoming Month" for anything as it gives inconsistent results because of the different numbers of days in the calendar months. So "Upcoming month" run on any day in February is effectively "Upcoming 28 days" (or "29" if it is a leap year), but will be "Upcoming 30 days" or "Upcoming 31 days" if run in other calendar months.

There is an issue CRM-16954 and associated PR which will, amongst other things, change "Upcoming month" to "Next 30 days" for 4.7.  I will canvas the idea of including "Next 60 days" in that PR, although there is a reluctance to add yet more relative date filters to an already very long list.

Finally to outline what will be possible in the near future. The aims of CRM-16195 is to allow people to define their own relative date filters through the UI.  We had hoped to have this ready for 4.7, but it is being pushed out to 4.8.  Quite a bit of work has already gone into this courtesy of Jon Goldberg.