Which nations have the best bonus to assist in a conquest victory?

Japan. While other nations have bonuses that certainly assist in producing an army, or movement of troops, Japan's bonus directly relates to combat. Since you'll be fighting a lot for a conquest victory, your forces will certainly be fighting hurt - and the ability to always fight at full strength certainly makes it the best option.

Japan is the best. However i find the mogal Keshik unit to be very good at taking down city defenses and can help in an early game conquest. Especially since they can move after attacking, so you end up moving in, hitting the city and then moving out of harms way. 2 or 3 will deplete a cities defenses to allow ground troops to take the city.