This has been bothering me because I am writing a Memrise course and have been implementing the romaji by hand for cases like these (since the Memrise platform interprets りょう as 'riyou'). Intuitively, I would think that 'ryou' would be correct, yet at the same time I've never seen りょお.
There are many different Romanization systems (ways of representing Japanese in Latin ("English") characters), which may represent the same sounds in Japanese differently.
The "correct" spelling of Japanese is determined relative to the system you are using.
To answer your question for りょう, the most appropriate choice is probably ryou. This is the standard way to represent this sound without using special character/diacritics in the Hepburn Romanization system, which is by far the most common Romanization system.
Hepburn Romanization has some variants:
In regular Hepburn, りょう would be ryou, with two vowel characters (o, u) put together to indicate the long vowel.
In Revised Hepburn, it would be ryō, with a macron to indicate the long vowel.
However, ryou is often the preferred variant because it doesn't take characters which may not display properly with some fonts or may be difficult to type (if you are making your own flash cards, for instance).
Other Romanization systems have different conventions. In the Nihon-siki system for example, long vowels are indicated with a circumflex, so as りょう is represented as ryô. In JSL, which is designed for teaching spoken Japanese, it would be ryoo, using doubled vowels.
Also, in reference to Memrise's choice of romanization: "riyou" and "ryou" comparison
There didn’t used to be small kana, so if you saw a word like りよう, you’d basically just have to guess if it was pronounced riyou or ryou.
Given, you could often guess from context, but anything that gives clarity can’t be bad, right?
After gendai kanazukai, you have りよう for riyou and りょう for ryou.