Tenants want a young dog and trying their best to persuade me to let them have it

Other

The tenancy agreement which they have signed states that they have to have the written permission of the Landlord (Which will not be unreasonably withheld)

This property has a garden. Would it therefore be unreasonable to withhold permission.
If I do give permission what should I ask them to sign and how much deposit should I take and does this deposit have to be protected. (I have already protected the deposit taken when they signed their tenancy agreement)
Your advice would be appreciated.