Do you mean a Carnet (Carnet de Passages en Douane ?? The CPD) as it is non trivial.
Unfortunately Thailand is not a signatory to the CPD system, as such they cannot / will not issue a CPD here. IF you can get a 'bike passport' the international travel document and romanized version of the Thai license plate a contact in the UK will issue a carnet on a Thai bike as long as the plate is romanized, they wont do so on a Thai scripted plate. Of course you still have to pay for the CPD and leave the bond as with any issuer.
I am unsure if the romanized plates from the Malay border that you can get would be suitable, I suspect they would be in a pinch, as the international bike transport book is now very hard (impossible ??) to get. Next time I go to the DMV here I will talk to the contact I have whose great with me and see if she thinks the international book is obtainable anymore. I am sure some of the posters on here know much more on that.