I don't know why people freaking say send an attack every 6 minutes.

KEEP CONSTANTLY attacking (as OFTEN as you can)

each attack after 15 loyalty increases public grievance.

If you have a 1/80 vs 1/99, which one do you think is giong to go to 0 loyalty more reliably?

Whenever capping cities, I spam cavalry (or archers if it's close enough and I don't wana lose cav) until it gets to 12-15 loyalty.

After that, I CONTINUE SPAMMING CAV. The only times I pause is when it gets around 5 loyalty (if the guy had his gates closed) so I can send a real wave to take out his troops.

I send so many attacks between 15 loyalty and 6 loyalty, that by the time my full attack wave hits the city to take out his troops, the city has already hit 0 loyalty, and I CAP the city on my attack wave without having to send more cavalry waves.