It is also to be expected that you will not unreasonably deny access.
It sounds like you definitely need to have a conversation with your landlord.....Start there.....
So I would recommend that you work with the landlord to allow showings safely with a licensed real estate agent in tow. The agent will discuss the process and work with you.
Also consider keeping the unit in good clean condition and not making it difficult. Many landlords did not want to be landlords in the first place. This may be there first chance to be able to sell the house considering the economy.
Playing nice (paying the rent on time and keeping the place clean and in reasonable condition) always comes back to benefit a tenant when you need the landlord to say good things about you.