Option A: The Water Clock
Water clocks were practically designed for dwarven use. Until the invention of the pendulum clock, water clocks were the most precise way of keeping time for millennia. A primary challenge with water clock accuracy is that the viscosity of water can change with its temperature, but living underground where the temperature is consistent water clocks could be easily designed to keep very good time. There can be fluctuations in underground temperature, but it is generally given that dwarves are sensitive to those temperature changes and so they would be able to tune their clocks accordingly (eg. make bigger/smaller holes).
A fun way to include this might be to hook it up straight to whatever water distribution system you have, such that each kitchen- or bathroom-like area could have its own clock.
Option B: Heated Object (for Dwarves with Heat-Vision Only)
Not every universe provides dwarves heat vision, but those that do posses that ability have a unique way of telling time. A trusted elder would be charged with keeping time and, at a specific time, would expose a large central column of a pure ore to a large heat source that would take all day to dissipate. Dwarves in the area could simply look at the column and understand whether the day was starting (very bright), ending (very dim), or somewhere in the middle. This could be very comparable to a human having the sun to look at.
(Attribution to the Dark Elves in Forgotten Realms, who use a similar system)
Option C: The Pendulum Clock
As others have stated, a pendulum clock is a very good way to keep time. Depending on the universe it may or may not be too advanced for dwarves, which is why I left it until the end.