Which modern day prop (piston) engines allow for inverted flight?
Any “modern day” piston engine can allow for inverted flight if it has the right equipment on it. 

The American Champion Citabria with the 7KCAB Inverted Fuel and Oil package along with the American Champion Decathlon are both "Modern Day" aircraft capable of sustained inverted flight. 

The major differences between the7GCAA and 7KCAB were in the fuel system and the engine oil system. The engine was replaced with a Lycoming IO-320-E2A of 150 horsepower (110 kW), while a header tank of 1.5 gallons—located beneath the instrument panel—was added to the fuel system. In addition, the carburetor was replaced with a fuel injection system, and a Christen Industries inverted oil system was fitted to the engine. All of these changes were made in order to allow for extended inverted flight, a mode not possible in the earlier models.

disciplesofflight.com/american-champion-decathlon/
You can fly inverted continuously for about two minutes before the fuel in the header tank runs out and the engine falters. Rolling upright will recharge a depleted header tank in about a minute while the faltering becomes a smooth running engine again