If they have API support for importing a private key that might work.
You don't need to import a private key, you simply use Blockchain.info's API to redeem the private key on behalf of your customer. Here's the API:
You would probably want to verify the amount of funds available to that address as if the amount is lower than the amount available, the change gets sent right back to the address it came from.
This could also be done with the Raw Transactions capability of the Bitcoin.org client v0.7 and higher.
So you never need to import the private key, you simply spend it to the address generated for a specific transaction and that takes the place of the customer having to redeem the funds themselves first.
Smart. Good use of the raw transaction API call.