While I have never played that scenario before... Some tips that might work.
First, how is your infrastructure. Do you have market places and happiess improvements built. If not, concentrate on defending yourself while these get built.
Two... give up on science for a while. Switch you tax rate to increase lux and money while lowering the science rate.
Three... do you have trade routes established. Have you been building any caravans/freight?
Four, use entertainers as a short term fix in the cities that really have happiness problems. This is not a good long term solution, but it can help until you can get your house in order.
Fifth... a cheat that works in some scenarios... If you steal or aquire a form of government from another civ that you are not allowed to used based on the specific scenario, revolt the same turn you get it... in some, it will bypass the restrictions and allow you to choose it.
Sixth... you didn't say what government you are currently in. If you are in Democracy or Republic, get your army into fortress and cities. Trying to keep a standing army on the field with either government can cause serious happiness problems.
I hope this helps. If you could provide some more information on your situation, I'm sure all the people here would provide more precise information to help...
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