It’s correct 😍 But when you speak it, you can give a little pause between hitam and dingin to make it sounds more natural like “Saya mau pesan kopi hitam, dingin.” or use yang as a filler “Saya mau pesan kopi hitam yang dingin.”

I would like to order an iced coffee, please!

That's grammatically correct and considered polite, but like what Rye mentioned, you can add "yang" right before the word of "dingin" to emphasize that you want a cold black coffee. It's really common among Indonesians to use that form. "Yang" in English could be described as "that" or "which".