To answer the OP'a original question, yes...for whatever reason, charge cards do seem to be more difficult to be approved for than a normal credit card.
Not sure why...especially since I personally find it MUCH easier to avoid digging myself a hole, since I have to pay the thing off every month! Surely an account with a 1-month repayment term must be lower risk than one with an indefinite term, statistically...
Anyway, get a credit product with Amex and maintain good account history on that for 6 months to a year, and you should have no problem getting approved for other Amex products.