Ujou, not Ujyou. You don't include a Y after the J, because the J already implies the Y.
For a more in-depth explanation as for why, in Japanese the vowel い (i) is actually pronounced closer to something like YI, that Y is just left invisible because it's also linguistically treated as a single vowel. Because of this, the invisible Y merges with certain consonant sounds to make what is written in Hepburn romanization as CHI, (TYI) SHI, (SYI) & JI. (ZYI) So you don't need a Y after a J, because the J already includes the Y. (If it didn't, it would just be Z.) Adding another would be redundant.
This is a phenonemon that happens occasionally in English as well, where it's called "yod collescence." It's why words like "nature" are pronounced with a CHU sound despite having TU written. (Because, in English, the vowels /u/ (Moo) and /ʊ/ ("put") especially when loaned from romance languages, are often pronounced with a similar "invisible Y," like in words like "user.")
So if you were to respell "nature" more phonetically, it would be something like "nachur" rather than "nachyur," right? It's the same thing in Japanese: JO, not JYO.
Though I guess it's also worth mentioning that in other romanization systems, like Kunrei-shiki, because じ is romanized as ZI, you do include the Y: ZYO, because in the first place it was the J that allowed you to hide it.