You've picked a particularly difficult region to find a reasonably priced flowmeter for.
Yes you can buy a E+H, ABB, Emerson Micromotion or Bronkhorst coriolis flowmeter which will measure this flow accurately- at a cost of many thousands of dollars. All these brands have a unit with a very small tube or tubes- less than 1/8"- and hence have a zero stability low enough to permit accurate measurements in the range you're looking for with reasonable turndown. The Brooks Quantim units are overpriced but do work also- to imagine their tube, think of a capillary tube about the size of a large paperclip...
At 100 mL/min you might find a liquid thermal unit which will work for pure water. Brooks has an old product, but Parker and Bronkhorst do too. Thermals will still cost thousands, but perhaps less than half the cost of a coriolis.
If you can tolerate a more modest accuracy and not much turndown, an oval gear meter might be able to do this flow for a few hundred bucks. It gives a pulsed (frequency) output, and will be blocked by any tiny particle of debris so a prefilter is essential.
If it's not deionized water, you might find a very small tube magmeter for this service, but turndown will be poor. Usually when we have small water flows like this it's water of sufficiently low conductivity that mags aren't an option.
I'd suggest based on our experience that you stay away from the laminar flow differential pressure units and the straight tube thermal units that some offer. Our experience with both these designs has been poor enough that we won't buy them again.