If the UK had lost World War I but the Ottoman Empire still fell apart an independent Iraq would probably have swallowed up Kuwait. In terms of stability, it might be a bit better off than historical Iraq with easier access to the sea and more petrodollars. In a German victory scenario it would also be the end point of the Berlin-Baghdad Railway, so it could even be a major global export terminal.
Another Middle Eastern country that could have been larger is the UAE, which tried to have Bahrain and Qatar join. It would have some stability problems though as Bahrain is mostly Shia (with a Sunni monarch) and does not have as much oil and natural gas. There would have to be a lot of transfer payments and a soft touch towards Bahrain to keep the populace happy.
There is also the possibility of Singapore staying with Malaysia instead of parting ways.