How do you write the following sentence with a defective verb in the past tense?: We could build the shed.
This sentence is already in Past tense (Past Simple).
If you wanted to transfer the sentence to a tense requiring Past Participle (like Perfect tenses) or Future tenses, you would have to use the structure to be able to. This structure has the same meaning as 'can' but unlike the verb has all forms and can be written in any valid tense. (It is usually not used in Continuous tenses). Then you would be able to transfer the sentence to any tense:
Future Simple : We will be able to build the shed.
Present Perfect: We have been able to build the shed.
Past Perfect: We had been able to build the shed.