I'm in South La. and almost any China, Polyantha or Tea Rose will thrive with little care, bloom often and experience little in the way of insect or disease. I have many roses, mostly antiques, and although it would be hard to narrow down a favorite easy rose I would have to include Katy Road Pink which I believe has been identified as Carefree Beauty. Huge bright pink flowers and almost always in bloom with no insect or disease problems.
My favorites which are easy, resist disease, bloom almost all year and are fragrant are:
China is Cramoisi Superieur
Bourbon is Souvenir de la Malmaison
Tea is Duchesse de Brabant
Polyantha is Perle D'Or or Marie Daly
Floribunda is Gruss an Aachen
Shrub is Thomas Affleck
Musk is Danae
cajunmama

The only rose I have that I almost never have to spray is the australian copper rose (climbing type). All my others need a good spraying program to guard against mildew etc.

I grow chinas, teas, and noisettes mostly. Louis Philippe is usually still blooming at Christmas. Rev de Or is a fabulous climber that has continuously bloomed for me this year, Monsiuer Tillier and Perle de Or, also continuous blooms. Several others that I don't have to spray, The list is quite long.

Betty

I have Baby Ballerina which is a rouring success for me, much better than Ballerina its parent. Mr. Bluebird and Blue Mist are good, and Red Cascade is so good I've given all of them away (but they keep coming back! Too much for me!)
I got a Summer Wine which is growing like mad as is my Gloire de Dijon and New Dawn. Those two root easily which makes them especially nice.
I have an old mini called Picayune (to distinguish it from other Picayunes it is Henrietta's Pink Picayune.) I have seen it in other gardens infrequently and in the 1912 book Everblooming Roses; I strongly suspect it is the Hwy. 60 Pink Buttons rose.
I have had some things die on me, but they were microminis and perhaps were just too tiny for the stress. Climbing Dainty Bess is pretty but still not very vigorous (nothing like New Dawn.)

I'm in Shreveport, so our climate is slightly different (read: LESS RAIN! :( ) However, I've had good luck with -

Don Juan
Perle d'Or
New Dawn (who wouldn't)
Windchimes
Duchesse de Brabant
The Fairy
Darlow's Enigma
Moonlight
Jeanne d'Arc

And if we could get some rain up here, I, and my roses, would be doing even better!

Tiffany and Belinda's Dream. I never spray anything except foliar feed, and these do very well, too.