Our private sector website, HouseSearch, includes adverts for properties which are suitable for a family to rent. These are normally 2 or 3 bedroom properties in the local area or neighbouring towns. If you visit HouseSearch run an intial search on the number of bedrooms you need (eg. for a three-bedroomed property); when the search results are displayed you will see that there are filters on the right-hand side of the screen, one of which is entitled 'Suitable For' and includes an option 'Families' - you can use this filter to display the properties which the landlords have indicated are suitable for families.
Using HouseSearch, if you are interested in a particular property that is not marked as 'Suitable For' families, you are still free to contact the landlord to express your interest and see if they might be willing to consider you and your family as tenants for the property.
Alternatively, local Lettings Agents may also be able to assist you in finding private sector accommodation for families.