The new law that lets the black plates go on any car, not just cars older than 1983, was signed a few months ago... but the DMV is slow on informing its workers. Car forums, facebook, and Reddit are full of stories of people getting turned away from the DVM when they try to get new Black & White Utah plates.
Here is all you need to do...
Go here:
https://mvp.tax.utah.gov/_/#1
Click 'Change your plates"
Enter your information to bring up your car..
In the "I want to order a" field select "Special Group Plage"
Plate Type: B&W Historical Support
Then follow the rest of the steps, enter your credit card info... and wait for your new black plates to show up a few weeks later.