What do I do if I cannot give a good reference to my PhD student?
A student who did the minimum during their PhD has very little chance of getting a prestigious fellowship.  In the sciences, you must have publications to get prestigious fellowships; a student who did the minimum will not.  Your role as a mentor is to guide students to attempt things they might succeed in.  Tell the student they will not succeed in this application.  Tell them to compare their record to past successful applicants.
You should not write the letter.  It will not help the student and it can hurt your reputation.  But you should have told the student that they would not get a letter for prestigious fellowships when you discussed their goals for completing their PhD.