I need a letter form that will allow me to give a restricted cash donation to a charity that can't be used for another purpose.

Nothing formal is needed; just say 'To be used for thus and such only.'
A charity that knows what they are doing will refuse it if they won't do that (and some won't, and there can be good reasons for not doing so). You could add a statement saying to send it back if they can't or won't comply.
Another charity might accept it and you won't have a way of knowing how they used it. Just because a group is non profit doesn't mean they operate ethically.
If you are talking a large sum, contact the administrators about it.