Yes, you can rent out your time without your cousin's permission. However, if your cousin takes issue with the fact that you are renting, he can take legal action. Depending on the circumstamces and any agreement that you may have, he may be entitled to a share of the rent that you collect. Also, he could go to court and file for a "partition" of the property.Pursuant to a partition, if a property can be physically divided the court will so instruct. However, where a division would be impracticable (as in the cse of a single family dwelling), the court will order a "sale in lieu of partition". In other words, there would be a sale of the property and an equitable division of the proceeds among the co-owners. However, before it would be so ordered, however, the court would permit one co-owner to purchase the interest of the remaining co-owner at fair market value.Bottom line, you may just want to work things out with your cousin, before things get out of hand. Partitions are costly and time-consuming.