European Pears bloom relatively late but before apples and sour cherries.  They are one of the easier species to grow, provided that fireblight resistant varieties are planted in areas that experience wet springs.  Pear scab, psylla, and blister mites can be a problem too, but the former two don't seem to be too common for home-growers and the latter is mostly cosmetic (although it can make the leaves on this species look very bad).  Varieties that are labeled "highly resistant" to fireblight have been reported to perform quite well in the deep south. 

European pears can take a very long time to produce, but there are rootstocks, such as OHxF 87, that induce early bearing and knock the expected number of years down to 2-5 (usually 3-4), depending on the variety.

Asian pears bloom earlier than European pears, and they may not overlap.  However, they produce smaller trees and begin bearing much sooner.  Resistance to fireblight and pseudomonas are often required for survival, but I do not recall hearing about scab or psylla being a nuisance.  Pseudomonas seems to generally occur on the first 2 or 3 feet of the tree, so grafting more susceptible varieties fairly high may help protect the tree.