Is there a landing gear system that extends automatically to prevent belly landing?
The simple fact is that an unintended gear deployment could be catastrophic, as it has a profound impact on the flight dynamics of the aircraft (one of the reasons there are warnings for both retraction and extension).

The benefits would be marginal as checking gear down is part of the bread-and-butter procedures for all retractable gear aircraft. 

Keep in mind adding some automation to an aircraft has far ranging impact, just off the top of my head adding automatic gear mechanism would require:


Standardization of the automation
Modification of procedures
Training of pilots, and then re-certification of pilots
Training of maintenance crews, and then re-certification of the crews
Possible change to the maintenance schedule of aircraft
Certification of the new system by the regulator


and you would still need a backup / redundant system; and now you are back to the manual controls.

I can imagine this being implemented in remote piloted or autonomous aircraft though; as an additional workload relief.