I'm David and I'm a Tour Leader for Portugal and Spain.
For me April/May are really the most flexible months. Is when you can have the best combination of good weather, flowers and places are not crowded.
[ Edit: Sorry, no promos please. ]
April, May and June
The weather is nice and you can avoid the crowds of tourists you would find in July/August.
I personally prefer October / November but April and May are great too.
Tulip season for you - April flowers and all that, and the tourists are still at home. Don't miss the wonderful cheeses sold on the dairy farms - yum!