There are no month-to-month renters insurance policies for tenants. Since renters insurance annual premiums are generally affordable, insurers may not find it economically viable to offer coverage for just a few months.
If you only require renters insurance for less than a year, such as when you've recently signed a six-month lease or plan to move out in eight months, your best course of action is to purchase a cheap renters insurance policy and cancel or transfer the policy to your new address.
Cancellation procedures and associated fees may vary depending on your chosen insurance company. Typically, you must initiate the cancellation process either online or by contacting your insurer. If you've paid your premium in advance or in full, you should ask whether they can refund the unused portion of your premium upon cancellation.