What suit can I bring against neighbor's for their dogs who has done damage to my property and is a threat to our well being?

File the dangerous dog petition..sue the landlord and the tenant for damages, damages to your dog and personal injury.

The first thing you need to do if it has not yet been done, is to send a letter to the owner of the neighboring property, keeping a copy of that letter for your records, for the purpose of placing the owner on notice of the dangerous dogs which the tenants have. Your letter should provide details as to each and every incident involving the neighbors and their dogs, further explaining your intent to hold the landlord liable for each and every future incident, if that owner does not evict the current tenants. Your letter could also point out that many insurance companies exclude pit bulls from coverage under a homeowners policy, such that the homeowner may wind up personally liable for your future damages. If that letter does not result in the neighbor tenants being evicted, then each time there is an incident causing you damage, you should file a small claims action against the owner of the adjacent home (so long as your damages are under $10,000.00). While it would not hurt to also named the tenants and any future legal actions, the tenets themselves maybe judgment proof.

Report the dangerous animals to animal control and the police. You could sue for a nuisance I suppose, but animal control and the police will be the cheaper way to go.