i had a similar situation and last year planted 'heavenly blue' morning glory and moonflower vine together. the mooonflowers are fragrant, big and white, opening in early evening and closed by the next morning when the morning glories open. on overcast days, both can be open.
i also grow a clematis named 'blue ravine' (pic below), which looks more purple than blue, but it only flowers for a few weeks in late spring. you might look into repeat-flowering types of that vine.
the moonflowers are more vigorous than the regular morning glories, growing to 15' or so, but can be wrapped up and down a vertical support.
i can't think of a blue-flowered perennial vine that would bloom all summer. maybe a repeat blooming rose?
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Beautiful pictures. Thanks for the helpful advice.

The clematis named Roguchi is an excellent repeater. It's blooms are bell shaped and a deep purple. It's one of those that you can just cut back to the ground every winter, which is far easier than the kinds you have to untangle and prune judiciously. It's also easy to find in the spring at gardening centers.

Another very easy flowering vine would be Purple Hyacinth Bean. You can start it a bit early in a deep pot and then transplant, but I ususally just stick the seed in the ground. It's utterly carefree and gorgeous when it starts blooming. Very easy to save seed from year to year too.

donnabaskets: haven't been able to find these online.
I tried Park;Burpee;Burgess;Springhill

for purple hyacinth bean, do a web search for it with the botanical name (dolichos lablab seeds). i saw several nurseries with them listed.
also, search for "clematis 'roguchi'". one source which has good ratings is plant delights nursery. you will have to buy the plant for this one rather than seed.

Select Seeds has both listed in this year's catalog and will be considerably less expensive than Plant Delights (Good Company. Just high prices.)

By all means just buy seeds for the hyacinth vine. It is ridicuously easy to start from seed.

You need to consider Passiflora (Passion flower)--some are tropical, but some are cold hardy to Zone 7. Absolutely stunning blue/purple flowers!

How about thunbergia gradiflora Blue Sky Vine? I am envious that you can grow much more in zone 8 than my zone 7. I always love Heavenly Blue MG, though.

Thanks for all the help.

Check out blue pea shell vine too.

I have seeds for it and also for purple hyacinth vine if you'd like some.

Here is a link that might be useful: Clitoria ternatea

Summerhill seeds has a blue Clitoria with double flowers!

If you do plant the purple hyacinth bean there are some things you need to know. First of all you need a very large trellis. Mine climbed up a 6 foot tall teepee and just kept going to eventually be at very least 15 feet long. And it was enormous. I kept wondering just how many seeds I had planted for the darned thing. Was shocked to discover after the frost had killed it back, that it was only a single plant. We love it, it is an absolutely gorgeous plant.

Now the bit you really need to consider. The ag people are warning about a very serious infestation of lablab bug.....and this is the lablab vine we are talking about. They are worried because the bug is attacking other legumes, and so there is concern for the peanut and soybean crops. Might do some checking first to see if the bug is in your area and/or if they are warning against growing it.
Dell

If it is a large trellis, I'd recommend Thunbergia grandiflora (Blue Sky Vine) -
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A less vigorous plant for a smaller trellis, you might like Thunbergia battiscombei (Clock Vine) -
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Both die back to the ground here in zone 8b, but regrow from the roots every spring. I've enjoyed both of them!