I would imagine if they have science, they would be able to mark the passage of their planet around its sun by shifts in the constellations at night?
If they're on the sunny side of a tidally locked planet, there is no night. Depending on the technology level of the world, they might not know the stars exist.
I think the first thing the OP needs to worry about is the idea of time. How does the concept of the passage of time register with people who do not have a day/night cycle, let alone seasons?
Heartbeats and breaths would be their first introduction to the idea of time passing, so a clock based on a standardized beat would be an easy concept for them to grasp.
But does their time system just keep running indefinitely, or does it roll over and start from zero at some point? And if it runs indefinitely, what's the starting point? Maybe, to keep appointments, the two people who want to meet have to "synchronize watches"--i.e. zero their clocks in unison, and then agree on a set number of beats later at which to meet.
A water drip clock would make sense to these people, as it's analogous to a heartbeat or a breath.
You can rig a water drop clock to just keep running indefinitely, or you can have one that fills a vessel of a standard size. When the vessel needs to be emptied, that's the start of a new "hour", so a finite-size water drop clock would eventually lead to the idea of time rolling over and starting from zero again.
(Note this would be a radical concept to these people. They'd be much more comfortable with the idea that time just goes on and on without stopping. That's what would seem "natural" to them because they don't have anything in their lives except for their own sleep patterns to think of as a reset point.)
A clock that resets to zero at well-defined increments, once it becomes common, would eventually be standardized by society, i.e. everyone would synchronize their clocks to some central standard (and maybe old-fashioned people would rail against this "complicated" scenario, grousing about the good ol' days when everyone just set their clock whenever they woke up.)
Once the synchronization has happened, then your society will start to develop analogues to the ideas of days, weeks, etc. There will be certain blocks of time that it will be convenient for people to talk about.
1000 seconds is roughly half an hour, and 28 hours is about 100,000 seconds, so a decimal system based on the heartbeat wouldn't be bad. People can talk about kilobeats of time. "Let's meet in a hundred kilobeats. The yoghurt will be ready by then, and I can bring you some."