Sounds very similar to Topher's cough that he had a few months ago. It would only 'act up' when he was settling down to sleep or rest, or when he was running or playing hard. I took him to the vet and lo and behold he diagnosed him with tonsillitis. He put him on an antibiotic for 14 days and it cleared up perfectly. The vet recommended that I give him a teaspoon of honey before bed, to help his tender throat. This really helped to ease the pre-sleep coughing.
I'd definitely take him to the vet to get it checked out. It could be one of many things so it would be best to err on the side of caution and have it looked at as soon as you can.
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