I requested my 61 day CLI today and i was approved.. My starting CL was $2000 and was bumped at $6000... You basically need to wait 61 day from the account opening (it could differ from your approval date so you might need to check your Quizzle EXP, Transunion or Equifax report to get your accurate opening date or you can also call Amex and ask for it)
This is my timeline:
-Approval date 12-17-2012
-Account creation (Opening) 12-18-2012*
-CLI request 01/17/2013
To increase your chances of getting approved for the CLI, keep your overall utilization under the 30%. Keep all your account current and don't open too many new accounts
You also need to have enough income to support your CLI
Not everyone will get approved it'll be based mostly in your credit profile.. They'll be softing your EXP report 3 or 4 times during these 61 days (its like you are on probation) So they might approve your full increase request, other times they might counter offer if they don't feel comfortable giving you the full 3X CLI or you can get denied (in that case you'll be able to request a CLI in 90 day)