Perhaps Morning Glories? With the morning sun...I know mine grow in partial shade. They grow fast...flower in the morning and will cover a trellis in one season.
I am trying Cardinal Vine for the first time this year but just planted seeds a couple of weeks ago and it has been slow progress so far.
Someone else will be able to make better recommendations than me....there are some real expert gardeners on this forum and I just play around.
I know many people grow Clematis...all the garden centers sell it....I have not so far had it as I just got my arch/trellis a couple of weeks ago.
My morning glories all grow on our fence and came over here from the neighbors yard....haha.
Good luck...some one will tell you just what to get I am sure.
G.M.

There are many lovely vines you could use.

If you want a fast-growing annual vine that would bloom repeatedly throughout the summer, you could try any of these:

Morning Glory, many named varieties, fast grower, morning blooms

Moonflower, fast grower, heart-shaped leaves, large white flowers that open in the evenings, lovely fragrance; starts bloomin in mid-summer

You could plant moonflowers and morning glories on the same trellis, and have blooms in the morning and in the evening.

Cardinal Climber

Cypress Vine

Purple Hyacinth Bean Vine

Black-Eyed Susan Vine

Scarlet Runner Bean Vine, fast grower but can balk at high heat

Mina Lobata--can be hard to germinate, but then grows quickly and has lovely flowers

Cathedral Bells aka Cup-and-Saucer VIne

If you want a perennial vine that will return every year:

American Crossvine--lovely, tough, fast-grower, loved by Hummingbirds

Sweet Autumn Clematis--sort of slow the first year, but will reward you forever after with lovely, sweet-scented blooms in August when you really need something lovely in the garden. Likes shady feet and at least partial sun. Worth trying again. Once established it is very tough.

Clematis--there are many lovely clematis vines that have beautiful blooms, but you will need to do careful research to find one that can survive our summers

Wisteria--fast grower, but doesn't know when to stop, and this vine is a monster, so be sure you really, really want it because once you have it, you can't get rid of it easily

Trumpet Creeper, Madame Galens--One very fast-growing, very tough vine. Orange tubular flowers. Sometimes this can be invasive, so again, be sure you really want it. If you plant one, be SURE it is a named hybrid as they are much less likely to become invasive. There is a yellow-flowered version called 'Flava'. I grow them both on a trellis and they have not been invasive for me.

Honeysuckle, Coral--a hummingbird magnet. This is the well-behave American native (Lonicera sempervirens) and not the invasive Japanese Honeysuckle.

Lonicera heckrottii--a couple of the named varieties are 'Goldflame' and 'Pink Lemonade'

Boston Ivy

English Ivy

Silverlace Vine and Climbing Hydrangea can be slow to get established.

Passionflower

Dutchman's Pipe

Climbing Roses

There are many others, but these are some of the more common ones.

Air Potato Vine is an old passalong plant that is very fast growing but is hard to find in nurseries.

Coral Vine/Queen's Wreath is only reliably hardy to zone 8 but is a beautiful fast-grower. IT will have tip damage at 32 degrees and will freeze to the ground if temps hit the mid to low 20s, but it is gorgeous.

Dawn