So far as I can research, all rivers on Earth are flowing water. There are other substances that are liquid at room temperature. Are there any natural processes that could create a river of something other than water? I'm not talking just emptying a reservoir... I'm taking like a grove of maple trees making enough syrup to canoe on (not plausible, just for example) or similar renewable cycle to keep the river flowing. I've been trying to design one with no luck. (Acceptable would be a natural pump that recycled the fluid back to the start. I only need it to flow about 50 km.)
The simplest answer is theoretically "yes" because there are many chemicals that are liquid at Earth's surface tempeatures.
But there aren't many (other than water) that have the right combination of all the attributes you need.
- Liquid at surface temperature & pressures (T&P)
- Available on the surface
- Evaporates at surface T&P
- Condenses at atmospheric T&P
- Light enough to be airborne at atmospheric T&P
Water isn't the most common liquid on Earth. Magma and the liquid iron we think is at the core are. Oil comes after water, if I remember correctly.
The problem is magma and iron don't remain liquid at surface temperatures and oil doesn't evaporate/condense in the atmosphere. So, no rivers.
As Dubukay points out in his comment, you can have temporary rivers, if there's enough volume. As you point out, there isn't enough maple syrup (a pity, that). I'm also a fan of honey, but there's not enough of it, either. Oh, and Willy Wonka's river of chocolate. But that's not naturally occuring (and that's the greatest pity of all).
Adding to this, you could use methanols, ethanols, alcohols, gasoline (not naturally occuring, but we'll include it), but they're all so volatile that they don't remain liquid very long and won't condense in the atmosphere.
It's really staggering to realize just how much water there is... and how magic it is... It's the goldilocks "just right" stuff. There's enough of it to consistently make rivers, it remains liquid at most surface T&P, it evaporates and condenses. It does everything you need to make a permanent river. And it's the only thing that checks all the boxes.
And I'm assuming that water-based solutions aren't part of the question, such as blood. But, frankly, there isn't enough of that, either. But it's worth pointing out that it doesn't count because it's just a water solution with something in it. If it counted, you'd need to differentiate between muddy water and pure water. So, "rivers of blood" must remain the provence of poets.
So, assuming what you're asking is whether or not it's possible to have natural rivers of anything other than water, the answer is no.
This Stack Exchange Answer describes some non-water materials that are liquid at room temperature. I'd say your best bet here would be oil or some type of hydrocarbon.
Maybe you have a natural oil well that happens to produce enough liquid that a surface pool forms and begins to flow downhill, like a spring-fed stream.
You could more easily make a stream or river that is some parts water and some parts your mystery substance. Rivers and other natural bodies of water are not 100% H2O; they contain impurities, silt, and tons of organic material.
What sort of properties you need out of your water feature would of course determine what substance you mix and how much is mixed in.
For example, perhaps your water source comes from a spring that contains a great deal of 6,6′-dibromoindigo, turning the water bright purple, or some other natural dye turning your river the color of your choice.
A river of urine would be feasible as long as there is a high density city upstream. Imagine a regular water river next to the city, which is used for water supply. Assume the residents or city planners don't want to pollute the river by dumping sewage into it. So instead the pipe the sewage over a small hill into the next valley over which happens to not already contain a river (of water). The sewage now flows down that valley, where it will either evaporate after several miles, or maybe will eventually reach the sea (or perhaps join up with the water river farther downhill)
Evaporation is only needed as part of the cycle if we assume a single substance cycle, but in this case the cycle involves, rain, water, human body, urine, ocean, rain.
Other more complex cycles involving syrup or beer may be possible as well. For example. A civilization has invented beer, and aquaducts, but not the wheel or the keg. The may brew their beer in the hills, and ship it by aquaduct (or "beerduct") down the valley to the port city. The cycle is now rain, water, brewery, beer, river, pub, human body, urine, ocean, evaporation, rain