This is a great question because the clue lies in the wording of the riddle and it is such fun to read through all the suggestions and see how easy it is to misread or misunderstand, in one way or another, the words.
Firstly, the original scene layout has been edited and we are pointed to understand that the instruction to "guess" is intended to mean "guess correctly". Lots of people have ignored that specific instruction and suggested that the mother only needs to make any guess.
We also have to make the assumption that in this imaginary scenario, the players in the scene are bound by the stated rules of the game and are not free to lie, cheat, trick or revert to behaviours typical of real mothers or real crocodiles. ANd also that everything stated, is there for a reason. We are told that the crocodile is slim - which could mean he will be very hungry and eager to eat the child; or it could mean that he values other things above eating; or it could simply be there to be a red herring. We have also been told that the crocodile is a solipsist, and so it is fair to assume that, being so, the crocodile will also be bound by the unspoken rules of his own solipsism. What does solipsism actually mean? - its a belief that the only certain thing in the world is one's own mind and that anything outside of our own mind cannot be proved to be real or exist. This is a clue to tricking the crocodile because he is limited by his solipsism while the mother is not, and this will be her advantage . However, I think many people have somehow misread or misunderstood the crocodile to be a philosophist, not a solipsist. .... .
So, let the game commence. 4 things have to take place, in correct sequence:1. the mother makes a guess 2. after hearing the guess, the crocodile then does something WITH THE CHILD, as stated (ie not alone,or independently of it) 3. what the crocodile has done with the child now reveals whether her guess was correct or not, and 4. as a result of her correct or incorrect guess, the crocodile then returns or eats the child. So all the guesses that "he will eat the child" or "he will return the child" are wrong because he cannot return the child after he has eaten it, so he will not return it, so the guess is wrong; and equally he cannot return the child a second time after he has already returned it a first time, so that guess is wrong too. Suggestions like "you will wait to hear my guess" or "you will open your mouth to eat the child" are wrong also because those are not things done WITH THE CHILD.
So my suggestion is that she will say "You will question whether my child exists" which will fulfill the criteria of being a solipsist, and of doing something WITH the child. So the fun of the riddle is that we are misdirected into thinking about how to save the child, instead of thinking about the meaning of solipsism. And now we understand why the crocodile is slim, because he never eats anything because he cannot be sure any external thing he catches actually exists. However, there is a riddle within the riddle, because in solving it, we are then reminded of our own solispsism. Because nobody told the mother that the crocodile was a solipsist. We assume she knows because we know, demonstrating that we consider all of the riddle to be part of our own mind instead of something external to it.