60Hz to 50Hz Conversion
I believe what you want is an online sinewave UPS built for the European market.  That will input don't care Hz power and output 50Hz power at all times.

We're not a shop-for-you site, so you'd have to go elsewhere for advice on which one.  

The important features are 


Online, which is a specific subtype of UPS, indicating output is inverter-driven at all times, using all-the-time double conversion, and it never bypasses and serves line power directly. 
Sinewave, to make the motors happy.
Output of 230V to satisfy your Eurogadget.  The input voltage does not matter, so bonus points if you can find one rated for  120V-240V input, and the ability to input varying voltages strongly suggests it is a double conversion unit.  
Listed by a Nationally Recognized Testing Laboratory. Most European testing labs are qualified bevause their standards are equivalent to ours.  CE won't qualify, it is not a testing lab, it is only a promise from the manufacturer, is widely falsified, and effectively stands for Chinese Excrement.