Good luck in your search, because I suspect it will be a long one, full of disappointment.
For reasons of power consumption, phones all use LCDs for their displays. Even when backlit, these tend to pale in comparison to the luminosity of the sunlight reaching the earth. So basically, short of someone coming up with a revolutionary new display technology, direct sunlight is ALWAYS going to completely overpower your phone's display. It really is just a case of a design tradeoff. If phone designers had a more powerful battery, they could probably put in a brighter screen, but that would mean making the phone much bulkier than people are willing to put up with today. So, short of some revolutionary new type of display or breakthrough in battery technology, the best thing to do is try and figure a way to keep the phone out of direct sunlight when you need to see it. Easier said than done, I know, but you're not likely to see the situation improve any time soon. No one wants to invest all that money into R&D to come up with anything. That's why we've been using LCDs for decades and there hasn't been much in the way of new battery technology in roughly the same amount of time.
Does anyone know of a cell phone model that has a large, easy to read display, even in direct sunlight? I have a Nokia 2610 that my 46 year old eyes just can't see! It is especially bad in direct sunlight, nearly impossible to see any text. I don't care about features, even gave up a Nokia 5300 because it had too many features. I just want to talk, text, and be able to see the screen. Any suggestions?