Is there a way for an aircraft to tell a ground station when the gear is down?
AFAIK, ACARS reports the block time and flight time already. That consists of parking brake release and parking brake set (block time), and weight off wheels to weight on wheels (flight time). These are to help airline maintenance keep track of when they need to do inspections, etc. It would certainly be possible to program it to report wheels up and down, but currently there's no reason to have it report those times. 

I'm not sure if you're talking about having this reported in real time or not, but automatic ACARS reports are not exactly in real time. They can transmit things right away (such as text messages from the crew) as long as they have a network connection. But the automated messages are queued for transmission as a block and some types of messages are prioritized over others. 

If you're talking about just collecting this data for later analysis, many aircraft are equipped with a quick access recorder (QAR) which records numerous flight parameters. I'm fairly sure wheels up and down times are usually collected. QARs are intended to give information about the flight that can be collected after a flight lands, either by USB, cellular or removable memory cards/disks/tapes. These are collected periodically, such as when the plane returns to the airline hub. This data is used by airlines as part of their flight data monitoring program which looks for incidents that exceed defined thresholds or trends that are occurring to help identify possible safety risks. So the airlines already have a method to collect gear position data.