Are they indoors or out? If it is warm enough outside they will do better there. Just keep spraying with water and knocking the plants gently with your hands. Aphids are weak fliers and crawlers and if you repeatedly knock them off the plants they'll reduce.

By the time you see any Aphids on plants there may well be several generations of the wee buggers there, so knocking off those you see only allows the next generation to move in that vacancy. A good sharp spray of water will knock them off the plant but spraying Neem on the plant will do little to prevent the next generation from moving in. Perhaps this article about Aphids will be of some help.

http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7404.html

kimmq is kimmsr

Note that I said 'Just keep spraying with water...' Vigilance and water will work. Neem is not harmless and is not an authorised pesticide in the EU. Recent studies have linked Neem products to bumble bee death. Neem article

I had aphids on my eggplant about six weeks ago, and sprayed them off the plants every day with water for about a week. So-far, there have not been any aphids on the plants for the last 5 weeks so I would say spraying with water worked for me.

I just use my hands and squish them. You can wear gloves if it freaks you out. Natural remedy, easy and free.