[archduck]

It's no different from "a nice time in the islands," "a runty pick of the litter," etc.

What's probably tripping you up is that "rest" is usually a noun that takes predicative adjective rather than an attributive adjective. It's more common to hear "The rest of my day was nice," but less common to hear "the nice rest of my day."

But despite the ostensible grammaticality of the noun phrase here, frequency still plays a huge role in determining what we deem acceptable, so it's not sufficient to argue as a counterpoint e.g. "a nice rest of your day" is perfectly fine like these other analogously formed noun phrases, checkmate ... Language doesn't work like that.

I'd argue that your point is actually best articulated simply as "it just sounds weird," rather than calling it any kind of flub, grammatical or otherwise.