I took a class in fire ant management and the points should be useful to you except the specific remarks about the fire ants. My wife ran into your problem and I treated them as I would the fire ants. This method has been successful against fire ants in our yard and I expect that it was successful against the black ants at the church where she was unfortunately weeding. Below is my previous post about fire ant removal:

The North Carolina ag extension agents have been giving classes in fire ant removal for a year or so. The gist of the class is the following.

The effective way to remove fire ants is to poison the ants with any of the slow acting types that slowly get carried to the whole colony including the queen. This completely removes the colony AFTER A FEW WEEKS. Generally these are distributed around but not on the hill on a warm day when the ants are foraging. Put a potato chip near the mound if in doubt; if the ants don't show up in 30 minutes they won't be around to pick up the poison until it gets damp and unappatising.
Also important; one should not indiscriminately poison all ants. Other ants are teritorial and will fight to keep fire ants away. They are your friends!

There is a formulation of Spinosad for fire ant control that is blessed by the organic folks. I've used it before and it does work, but it takes a while. You can buy Amdro (not considered organic) at any hardware/home improvement store and it works a tiny bit faster.

The problem with any of these chemicals is that the sprinkle bait can be attractive to birds and it will harm them too. My yard is very "birdy" and so far I have not had any problems.

Another problem is that whatever is making your yard attractive to ants (in my case it is fire ants) will continue to attract ants. You might win the battle but you won't win the war. Kill whomever you can but a new group is ready to move in.

My garden is so overrun with fire ants that I have to block out an hour or so each week to do nothing but focus on the problem and even then I cannot get in front of it. They drive me crazy!

Widd,
Amdro will kill the ants for you. There is also another treatment that you can buy, just check for it at HD, you use your hose to spray it on, you can spray it on your whole yard. it kills ants, grubs, fleas, other nasties.
Since this is out front of your house, I would buy the spray, it covers 5,000 square foot for about 10 bucks.
The ants are coming for the moisture.
Something out front is nice and wet all the time.
Check your gutters to see is they are working properly the next time it rains. The water may be blcoked and pouring onto the front garden, and even into the lawn in places.
Ants LOVE moisture.
Just a thought.

Thank you for your replies. Butterfly4u, you're right about the front lawn being wet. Actually the whole garden is for a variety of reasons. The house is right next to a drainage ditch. A ditch that didn't dry up in the 5 weeks of no rain (except one tiny sprinkle) in June/early July this year. We've had nice consistent rain since then. We're also only a couple of feet above sea-level and about a mile from the Intracoastal Waterway. And yes, the gutters aren't working properly. They're very clogged up with pine needles. Getting them cleaned out is on our list of things to do. We moved in May and that list is 10kms long. LOL

Gardening here is a little different to the garden I had in NC. There the clay was packed so hard not even fire ants would invade. Here, the ground is moist and made of fine beach sand. It *bounces* when you walk on it. It's like walking on a dance floor. I'm lucky in that it's rich and loamy beach sand, but apparently the ants think they're lucky too.