I don't know how large your plants are but I usually just hold the stem and squish them in my fingers. You may also try sprayng them with a soap and water spray which prevents them from flying, or washing them with a fairly firm jet of water which flicks them off. They are very fragile creatures and don't usually need any toxins.

I've had them badly on large plants. They are difficult to control because they are on the underside of leaves. The spray or whatever you want to use doesn't get to the insects. One also has to be concerned with poisoning the bees. I don't have a good solution on large plants/plantings.

Answered on your other post on the Vegetable Forum. But also a question: Are they actually having an adverse effect on your melon crop? Or is just an aesthetic thing?

I've had them so bad the leaves curled up. In that case on large plants blasting them with water won't help and might cause more harm than help. This time of yr the plants better be big or you won't get fruit anyhow. I hate to say it but a systemic insecticide might be the only way to kill them. And on a plant like watermelon that's not an option either for me.

I thought I read that soapy water sprayed on them would kill them. Like Dawn and water solution.

You have to control your ants - they farm aphids.

You might consider buying some ladybugs. Ladybugs love to eat aphids. If you do this, however, don't spray any pesticides ahead of time because it could either kill the ladybugs or cause them to leave the plant and go elsewhere. Ladybugs are available at many local nurseries.

If that doesn't work, you could try and spray neem oil or insecticidal soap. I prefer neem oil because it works a little better, in my opinion.