I have no experience of the situation in Menorca but I know that on mainland Spain, companies which hire out child car seats tend to be those which specialise in the hire of wheelchairs, disability scooters, etc.
Many of them hire out cots, buggies, car seats and various other baby/child equipment in addition to mobility aids. In Benidorm for example, child car seats can be rented for €3/€4 per day or around €20/€25 per week.
If any of the Menorca regulars can suggest any mobility aid rental companies, it may be worth checking if they also hire baby/child equipment. But as Dave suggests, it may be worth comparing rental costs against purchase prices.
David