There is not anywhere in the resort itself im afraid! You could try enquiring at the complex's reception if it has one or who ever you pick the keys up from. You can always purchase or borrow a travel cot off a friend. They usually count towards luggage allowance (check with airline) In all honesty this probably the only way!
Have a fantastic holiday, the resort is one of the most beautiful I have ever seen and had the pleasure to work in. I went to menorce in June and went to Santo Tomas and nothing has changed since 2000! The beach is ideal for little children ans the resort is quiet. I would recommend hiring a car especially as your in a villa. The cost of food and drink is so much cheaper out of resort and the choice more varied.
Enjoy