I fear that there is not enough to go on here to identify a specific book. However one book that fits the right time frame, and is definitely centred around the construction of an evil pyramid is "Threshold" by Sara Douglass.
The protagonist, Tirzah is an enslaved craftswoman with a special skill with glass. The greedy Magi of Ashdod are building a giant pyramid that they intend to use to gain vast magical power & immortality. They are using armies of slaves to build their pyramid (at least 8 generations so far). When Tirzah touches the glass on the pyramid she can hear it scream to her.
Needless to say when, roughly half way through the novel, the pyramid is completed, it does not turn out the way that the Magi expected.
The novel was written in 1997. The plot is centred on the construction of a pyramid, which is definitely evil both in the lives lost to build it, and the slaves sacrificed to power it. The pyramid itself becomes alive in a sense (inhabited by an evil spirit).
All of those match. But the pyramid is not described as being obsidian. It is glass laid over stone. Nevertheless it looks quite dark in the image shown here. It seems possible to me that you remembered it as obsidian, especially since obsidian is volcanic glass.
![Cover of threshold around 2000](https://cdn.statically.io/img/i.sstatic.net/cKjri.png)