"Little Gem" magnolia doesn't litter, unlike most magnolias, but it is a slow grower. But if the corner you want to fill is far far away from your pool, you might try a standard magnolia grandiflora. They grow fast if watered and provide great privacy if you have the room.

Nellie R. Stevens Holly can make for a nice thick tree but most are sold as bushes, without the straight leader needed for a specimen tree form. But with some looking you might find one. There are other tree form hollys too.

Leyland cypress tends to get knocked over by hurricanes. Golden Globe arborvitae (I hope I got that name right) is very thick and can get ten feet tall and does well in sunny locations. Walmart carries them.

I planted Leyland Cypress 2 years ago for that purpose and have been extremely pleased. My "backyard neighbors" are on a slightly higher level so I wanted something that would grow tall. My smallest one is about 7 feet tall and 5 feet wide at this point and have taken very little care up to this point.

Bamboo, clump ONLY.
Grows fast and has the tropical look (evergreen)
lynn

I had a similar problem. I removed the fence around my pool when I had the deck redone. I wanted a privacy screen close in so I used a combination of things.

I made 5 trellises from 4X8 vinyl lattice and put them on landscape timbers about 2 feet above the ground and kind of framed them. Basically this made an 8 ft wide trellis with the top about 6 ft high. On two of these, i put Lady Banskia roses..they are evergreen. One one I am growing Confederate Jasmie and one one Carolina Jasmine (which isn't as thick a screeen as the confederate). The 5th trellis has another climbing rose but isn't really a good screen. I sort of placed these trellises at intervals around the deck toward the corners but not exactly symetrically..

In between these are a variey of other plants, viburnum which makes a bigger lush tree and lorepeltum for it's rich red coloration. The bed around my deck is of varying width from maybe five feet at the back of the pool to 10 feet on one end. So I also have room for compacta and some other hollies as well as day lillies, a few sago palms etc..
I used this other stuff for a low to the ground screen but also to give some texture /color differences. I've been shaping these other plants, some round, some square etc..

I'm definitely not a gardening artist, I just like to play and add stuff, but the effect is nice.