Did Aphrodite and Hephaestus have any children?

No, Aphrodite the beautiful love goddess and Hephaestus the blacksmith god had no children. But they each had children through other involvements. Specifically, in the case of Aphrodite her children were as follows:

With Ares the war god

1. Phobos;

2. Deimos;

3. Adrestia;

4. - 9. The Erotes

Eros;

Harmonia;

Anteros;

Himeros;

Pothos;

Hedylogos.

With Poseidon the sea god:

1. Rhode.

With Hermes the messenger of the gods:

1. Tyche;

2. Peitho;

3. Eunomia;

4. Hermaphroditos.

With Dionysus the wine god:

1. - 3. The Charites, or the Graces

Thalia;

Euphrosyne;

Aglaea.

4. Priapus

With the mortal Adonis:

1. Beroe.

With the mortal Prince Anchises of Dardania:

1. Prince Aeneas.

With the mortal Argonaut Butes, King of Sicily:

1. Eryx.

Specifically, in the case of Hephaestus, he had no children with Aphrodite or with Gaia. But he did have chilldren with Aglaea:

1. Eucleia;

2. Euthenia;

3. Eupheme;

4. Philophrosyne.

But the list changes according to the source authority.