The best way to beat the next step, is to take the next step.
I remember regent being a challenge, until you get the hang of using the tax slider, and the luxury sliders well.
Use the luxury slider to keep people happy, instead of using clowns/entertainers/Elvis. Use the tax slider, that if you are soon to research a tech (4 turns and less) move the tax slider down and still get the tech in the same amount of turns, but running a bit of a (bigger) profit.
Using and getting the Philosophy/Republic slingshot will also greatly give you an advantage over the AI - you will find a civ that starts with Writing to be good for this.
Regent is fun, as the AI has a bit more money (that you can get from them).
I've gotten much, much better than I used to be using the tax slider to get as much as possible while still getting. My last game (I just won Spaceship with Koreans/Warlord/Standard), though, once I hit Modern Times I had trouble having enough gold to research @ 4 turns ... in fact, despite being Commercial/Scientific, I always had trouble with gold, something I never experienced with Greece (also Comm./Sci.) ... contrast my previous game (Mayans/Warlord/Small), in which I had an obscene amount of gold and nothing much to spend it on (rushed a lot of projects on that account, though).
I have only used the luxury slider when necessary, though, because of the expense (apart from my previous game as Mayans, see above) and its effect on research. Of course, if I can get more income from the AI (something that was indeed less of a problem at Warlord, but still an issue), then that will make a substantial difference.
I started using the Republic slingshot every game, as soon as I heard of it, and I then just stay at Republic for the rest of the game. Much fewer problems with war weariness than Democracy, which used to be my go-to government.
I'm thinking I'll start with Iroquois, which is Agri/Comm and starts with Alphabet & Pottery, which should help for growth and a little extra gold. Picking AI opponents, however, is always a bit more challenging...