Dear Vowel Lady
i remember you.

hi.
i can't think of a particular card/program, but banks that offer credit all do so with varying parameters, based on one's credit history.
i would start with your bank. see if they are agreeable to opening a credit line with a specified limit, and setting it up so there are
no automatic increases. you could open the card in your name, and add her as an additional card holder. this way, she will not be able to make/request any adjustments to the credit line. the card would be billed directly to you, however. if you do it with your own bank, they will likely have a feature whereby you can link it to your bank account. this will make it easier to pay it, but this does NOT mean overdraft protection, which is entirely different.
generally, credit cards do not like to be prepaid. you can't leave a positive balance on most. they will cut a check and reimburse the following month.
another thing you could do is open a separate account in her name, and get her a debit card that is on visa/mastercard circuit. this is different from a credit card. no interest, no bills. but some banks offer debit cards that you can use the same way as you would a credit card.
another alternative is a "prepaid" credit card that is guaranteed by you for a fixed amount. i have only heard of these. generally they are done for people who have no credit history or bad credit history. an amount is placed on deposit and the credit limit is established based on that amount (usually equal to that amount). the account behaves 100% like a credit card. the guarantee deposit is not used to pay down the card... unless the holder defaults on payment...
if your bank doesn't have any convenient offerings, i'd just start visiting other banks in your area. the bigger ones are likely to have more offerings but may also be less flexible.
you could also consider AmEx. they are a charge card and not a credit card, and do not specifiy a limit. but they market themselves for "personalized" service - you might be able to specify conditions under which she can use the card. down sides are that AmEx is less widely accepted than Mastercard or Visa, and the annual fee is quite expensive.... even a second card holder is expensive.
~ waves ~