Since Contact is parent for Customer_Address__c Object, there might be case that one Contact can have multiple Customer_Address__c Object.

So replace this line:

Customer_Address__c customerAddress=[SELECT ID,Customer__c,Customer_Address_ID__c FROM Customer_Address__c WHERE Customer__c =:contact.Id ];

With:

List<Customer_Address__c> customerAddressList=[SELECT ID,Customer__c,Customer_Address_ID__c FROM Customer_Address__c WHERE Customer__c =:contact.Id ];

Since Contact is parent for Customer_Address__c Object, there might be case that one Contact can have multiple Customer_Address__c Object.

So replace this line:

Customer_Address__c customerAddress=[SELECT ID,Customer__c,Customer_Address_ID__c FROM Customer_Address__c WHERE Customer__c =:contact.Id ];

With:

List<Customer_Address__c> customerAddressList=[SELECT ID,Customer__c,Customer_Address_ID__c FROM Customer_Address__c WHERE Customer__c =:contact.Id ];

Also in your test class you're not creating customer_address__c data. That's why you're getting that error. Add below lines after inserting contact in your test class:

Customer_Address__c  customer = new Customer_Address__c ();
customer.Customer__c = contact.id;
customer.Customer_Address_ID__c  = 'customer Id';
insert customer;