While not explicitly depicted within the original Inuyasha anime or manga, it is highly probable and widely understood that Koga and Ayame did have children after they settled down.
Koga and Ayame's Relationship and Future
Koga, the leader of the Eastern Wolf Demon Tribe, pursued Kagome Higurashi for a significant portion of the series. However, he was eventually committed to Ayame, a fellow wolf demon who had a childhood promise with him. Their eventual union and decision to settle down are widely accepted developments in their story arcs.
The Likelihood of Offspring
Following their decision to build a life together, it is strongly suggested that Koga and Ayame most likely had children. This belief stems from the natural progression of their relationship and the desire among fans and commentators for their lineage to continue. The idea of their offspring emerging to assist in future adventures or sequels, such as Yashahime: Princess Half-Demon, was a fitting and anticipated development for the series' continuation.
This common understanding emphasizes that while direct on-screen confirmation of their children might be scarce in the original narrative, the context of their settled life implies a family, making the existence of their children a very strong possibility within the Inuyasha universe.