The idea of a simple park chair doubling as a sophisticated solar observatory is a fascinating concept. However, the direct answer is no; there are currently no public park chairs equipped to measure coronal mass ejections (CMEs). A CME is a massive burst of solar wind and magnetic fields rising above the solar corona. Measuring these events requires highly specialized and sensitive instruments, such as coronagraphs on satellites like SOHO or DSCOVR, which are designed to block out the bright light of the sun to see the fainter corona. These devices are complex, expensive, and not integrated into public furniture.

The confusion might stem from public art installations or educational displays that incorporate solar data. It is conceivable for a park bench to be connected to a data feed from a real solar observatory, displaying information about solar flares or CMEs on a small screen. This would serve an educational purpose, raising public awareness about space weather. Furthermore, the concept touches on the growing field of citizen science. While a chair itself cannot take measurements, a network of simple, ground-based sensors for monitoring space weather effects could be deployed in public spaces. These sensors might detect secondary effects of CMEs, such as changes in the Earth's magnetic field during a geomagnetic storm.

In conclusion, while a park chair with built-in CME detectors remains in the realm of science fiction, the underlying idea of making space weather data accessible in public areas is both innovative and achievable. It represents a bridge between advanced astrophysics and public engagement, potentially inspiring a new generation of scientists. The real measurement of these solar phenomena will continue to be the domain of dedicated space-based observatories, but their data can certainly be brought down to Earth for everyone to appreciate, even from a park bench.