I can't help you with South America but I spent April and most of May in Central America and Mexico.
Heading down the West Coast of Mexico in early April, it was sweltering hot (40 degrees at times) with no wind and no cooling rains. Locals told me that this was the hottest time of the year down there. But the mornings weren't too bad.
Into Guatemala I experienced mostly overcast and a fair amount of drizzle with pleasant temperartures in the Western Highlands, which changed to humid, sunny, and hot through the south of Guatemala, into El Salvador, Honduras and through all of Nicaragua.
The first real rain I encountered was in Costa Rica in late April. From there to Yaviza, Panama and back I had almost daily downpours. Some were the well behaved ones in the afternoon but there were also days of constant downpours. I was told that the rainy season had arrived early.
Panama also had regular downpours, with low clouds and drizzle in the northern highlands.
On the way back (mid May) there was definitely a change in the amount of rain through parts of Mexico. Mostly in the central highlands surrounding Mexico City. Northern Nicaragua was quite wet but the south was still bone dry even though I experienced daily drenching downpours in northern Costa Rica only several hundred km's away.
But overall, there were plenty of good days as well.
Through the various conversations I had with locals my understanding is.
April: Hottest time in southwestern Mexico
May: wet season begins (hit and miss)
June: Getting wetter and wetter
So my best guess would be:
April: hot and humid
May: mixed bag
June: more and more rain
Lowlands = hot
Highlands = cooler
Check out "www.lonelyplanet.com". They have a "when to go section" for all the countries down there.