(the easy answer is to only use divergences which sync with the established series info; the difficult answer is to try to make new episodes - not variations on canon eps - which rely upon the changes; or the third answer is to use a different show: one which would be easier to handle the changes - ie Burn Notice or Foyle's War instead of Numb3rs)
The further back in time you go, the more you have only three choices - but if you can think of more options, you're smarter than me...
1. strict adherence to cause-and-effect (ie, a US victory in Viet Nam would affect Alan & Margaret Eppes, Millie, and the Ramanujan family -- but none of the others would ever be born, or at least none of the others would be at all recognizable)
2. keep the change far from the scene (ie, if the Tamils are not driven to Civil War, it affects only the Ramanujans - do they still move to the US? - and maybe Colby up in Afghanistan)
3. use a semi-permeable membrane (ie, Japan, not Germany, wins WW2 against the Allies, yet Don Eppes is still the government employee we know and recognize in Southern California)