I think it'd be neat if golden ages were tied into active choices made in the game and that kind of choice makes whatever it is you did better for a short amount of time. Each time some milestone is met, there's a chance that your civ enters a golden age. After that, it's harder to trigger a golden age based on that same event.
For example, one condition for a golden age is getting back-to-back eureka bonuses. When this happens, there's a xyz chance of entering a scientific golden age where science is increased by xyz for xyz turns. After it's finished, the chance of a back-to-back eureka bonus triggering a scientific golden age is lowered by half, and then half again etc.
You could incorporate other factors in said example as well. If you want to balance it out a bit, how technologically advanced you are (or not) could play a factor. Civs that are behind have a greater chance. Civs that are in front have a lesser chance. With a player losing militarily, it could trigger a "last stand" bonus. The last player to found a religion, gets a faith production bonus.
Some other ideas would be -- multiple military victories cause a small, temporary combat bonus. Great people spawning can trigger a religious, science, cultural, money golden age. Founding a religion causes passive spread to be increased and/or more faith production. Certain wonders completed can trigger certain kinds of golden ages. Reaching a certain tech first causes a golden age. Being the first to adopt certain government types cause golden ages. Max reputation with a city-state causes a golden age. Finding natural wonders cause scouting units to gain +1 movement.
There could be a ton of others, and obviously, they'd have to be balanced, but it would build upon the whole eureka! bonus idea where doing something actively in the game is connected to a related bonus in a different system.