Harbor Freight Tools sells a wireless driveway alert system for $17.99. I have one that I haven't yet installed, and I don't recall any mention of a sensitivity adjustment. It isn't a "beam" -- it's an area coverage, just like the interior motion sensors in my home alarm system. For the interior sensors, when my significant other brought a dog into the household we had to have all the interior sensors replaced with less sensitive models that wouldn't be set off by a dog, but will still detect a human.
The HF "system" doesn't operate a light or interface with an alarm system, it just activates it's own, dedicated beeper.
For the price, I guess you just have to accept the occasional false alert if you have animals scurrying around your estate.