Can I purchase and register a motorcycle in Bangkok using a Certificate of Residency obtained in Pattaya?

You can theoretically get a COR from your embassy.

My Norwegian embassy issues a residence certificate at the address at which I am registered in Thailand. I do not know what practice your own embassy has. But if it's enough to just state an address in Thailand, you have the option of getting a residence certificate. But the problem with DLT is that you don't have a Non Immigrant Visa.

This article from Bangkok Post deals with the purchase of a car, but the same documents are required to buy a motorcycle,

8/how-to-buy-a-car-in-thailand-and-insurance-formalities

Note if a new bike /car you'll probably need to get a second residency cert one issued.

First to buy the bike and start the registration process.

Second when changing to white plates off red.

Each one is valid for only 30 days

No you won’t get

One in Pattaya on exempt

I sent you a DM

You can't use a COR outside of the province it was issued in.

So no you can't.

I've no idea if Jomtien are still issuing a COR on a visa exempt entry.

Many immigration offices have and are stopping issuing them.

Your resident certificate is your address. If you get a resident certificate from chonburi it will be your chonburi address. The moto will be registered to that address and province. You will need to complete the process in chonburi as you will be issued a chonburi plate.