Can I insure a manufactured home that I rent out?
Yes, with the right carrier. Manufactured construction and non-owner-occupancy each narrow the market and together they narrow it considerably, but it is placeable. If you have been told it cannot be done, it was probably not shopped widely enough.
What will they ask about?
Year of manufacture, whether it is on a permanent foundation, the condition of the tie-downs and the roof. Those four decide both price and appetite. Having the answers ready makes the process straightforward.
The home is in a park. Does that complicate it?
It can. The park agreement may restrict or prohibit renting the unit out, which is a contract matter rather than an insurance one. Settle that first, because no policy makes a prohibited sublet permissible.