I brought my tropical hibiscus plants inside in October (I sprayed them with insecticidal soap before I brought them in). I inspect them every few days for pests. Suddenly a few weeks ago one plant had small black dots under some of the leaves and clusters of the black material around new growth or buds. I can easily remove the black material with my finger. To date I have tried a pyrethrin based plant spray and I also tried insecticidal soap but after a few days the black material returns. I have neem oil if that is also something I should try. Thank-you.
This looks like aphids. Aphids can be tough to control as the life cycle can be rapid. Aphids are sucking insects and produce a honeydew as they feed. The black material sounds like a honeydew that fosters the growth of a black sooty mold.
Insecticidal soap sprays will kill aphids, but the insects must come into contact with the soap to work. You could try taking the plant to the bathtub or sink and hose off the insects (put foil or some other protective material over the soil in the pot so it doesn't splash all over.) You could also cut off the stems with the most aphids on them to reduce the populations. Dispose of in a baggie and isolate the plant from your other houseplants. Make sure the insecticide you use is labeled for houseplants and Follow all label directions of the product that you use. http://extension.umd.edu/hgic/plants/aphids-houseplants