Each new opportunity will have tenants who spot a possible way to make some money on the side and the advent of AirBnB is no exception. As an owner you may see no harm in the tenant letting out an extra bedroom in your rental home, but do check if this has implications with your local council and also with your insurance company.
Our local council – QLDC, have mixed use rates for owners renting their homes short term as visitor accommodation. There are other legislative requirements and implications for short term holiday homes – see http://www.qldc.govt.nz/services/rates/visitor-accommodation/
If your tenant is letting out a room then legally he becomes the landlord to his tenant with its associated responsibilities. It could get messy.
We would not recommend allowing your tenant to use your rental home for this purpose. A well-drawn up tenancy agreement will have a clause stating “Tenant may not sub-let or assign the tenancy”.