Go to amex website and search "transfer credit card" in help.
# Why can't I transfer available credit between my personal and small business credit Cards?
Given the differences between our personal and small business products, we do not allow transfers between those accounts.
# Why aren't all of my Cards eligible for a transfer of available credit?
Only your credit cards with enough available credit are eligible for a transfer request. They must also meet other criteria which may include account status, recent transfer requests or type of...
# Why can I only transfer available credit to between two Cards?
You can only request a transfer between two Cards once within a 30 day period. If you'd like to submit a request for another Card, please wait at least 30 days.
# Why can't I request a second transfer of available credit if I have already requested a transfer between other Cards?
You can only request one transfer within a 30 day period. Please wait at least 30 days since your last transfer to submit a new request.
Amex Credit Line Reallocation - Again available 
Sound the bell! Amex is now reallocating credit lines again!
I called customer service for my Amex SPG yesterday and asked if I could move $5,000 of my credit line from my Amex Hilton. The agent said there's a new program to allow if it the accounts "qualify"; he put me on hold, asked some questions, and a minute later it was done!
Yup, it can be done at least as of yesterday. Been calling for a few months and actually called this time to cancel my Starwoods cause I was fed up w/ it, and they transferred almost all of my Delta (that I never use) credit line to the Starwoods.
Programs: AA EXP (1 MM) | BA Silver | SPG Plat | Former EK Gold, CO Plat and AF Gold | Global Entry
Amex Credit Line Reallocation - Now Available (again)
Thought this might be of interest here.
I recently called in to reallocate my credit line from my old Blue Cash account (which I barely use) to my SPG card. Tried doing this in 12/2010 and 01/2011 to no avail, with agents claiming it would be available "soon". Apparently it is now available.
The agent also explicitly confirmed that this is not processed as a credit line increase request, and there is no pull on your credit or Amex-specific history.