I am thinking about starting a rental car company in my area a region that is fairly underserved. My fleet will be very small (i.e. less than 5 cars) and the people renting them will, for the most part, not be very wealthy. As a side note some of the cars we may rent out will be leased or financed from a regional dealer.
I have a lot of experience working with specialty insurance brokers who can build custom policies if necessary depending on what you are trying to build (eg, new carshare, rideshare services).
If it is a traditional car rental program, you'll need to find a broker who provides that type of insurance. You could try asking local rental companies who they work with and ask for a referral. Having a small fleet and working with low income populations (eg, possibly no credit cards) adds some risk and challenge for getting set up. You said "some" of your cars will be leased. What about the others? The first question you need to answer is 'who owns the cars'. If you are trying to do something peer-to-peer, it will add cost and complexity and there are fewer options for who you can work with. I'd suggest doing one or the other and avoid mixing the two.
Happy to discuss in more detail on a call.