How did Goten and Trunks become Super Saiyan so easily? Most Saiyan (Goku, Vegeta, Gohan, etc.) who evolved into Super Saiyan had trouble fulfilling one of the requirements to evolve: Their rage or other emotions had to be extreme.

However, there are two exceptions: Goten and Trunks (not the Trunks from the future). How did they achieve it? They hadn't seen or done anything that could drive them to such a level of rage/intense emotion to allow them to turn into Super Saiyan.
According to this Yahoo answer:

Because by the time they were born Goku and Vegeta had already been Super Saiyan and with the higher power level thus when trunks and goten where born their levels were also higher.
Think about it this way Vegeta (Fut Trunks timeline) was weaker at SSj Level so Future Trunks took longer to become ssj (i think he was 13) while Vegeta (regular DBz timeline) had trained harder by knowing the androids arrival 3 yrs prior to chibi trunks being born thus more powerful ssj1 vegeta. And Goten being born around some time near end of the Cell Games saga Goku had became already full power ssj.
Thus as children their power levels were already exponentially higher than the latter of gohan who was born back when goku was weaker in power level.

Basically Chi-Chi gave birth to a Demigod.