Not sure where you are, but if in Bangkok, the process to get a Certificate Of Resident, they put it in the post. It took Thursday - Tuesday to get it.
I went to DLT in Nonthaburi / Pathum Thani / finally Bangkok province to get it. None, I mean none of the DLT took my Yellow book as proof of resident here, they all give me a requirement paper, and they all required a COR from Immigration department.
I came from Toronto a few days ago, and Thrifty / Hertz / there would not take a Thai DL unless you have a Thai IDL. They told me it is the law in Canada. For me, I have (3) other valid DLs, but my spouse had only Thai, and she was not able to go on the rental application.
At the DLT, you would see a sign stating "Walk-In", but honestly that line is for Thais, because I tried and was sent out the line.
My wife and I have learnt our lesson, to always have a valid Thai IDL if traveling with a Thai drivers license.