I don't know what can be done with existing security company boxes to program other numbers to dial, but there are unmonitored DIY alarm kits that are pretty good for the price, where you program which phone numbers you want it to dial during alarm. The wireless sensors are very similar to what some major name alarm companies use.
X10 is the main one I recall, and I think there are other brands that they sell in stores like lowes, target or best buy. Probably amazon or ebay has a few. Not sure if they still do it, but x10 used to have weekly "blowout" deals where prices would be much lower than listed retail, and they make it sound like some crazy extreme once in a lifetime sale they are having, but they actually just do it all the time. You just need to wait and look around for the sales. I remember them selling kits with the base console, 10 or more window/door sensors, a few motion sensors, multiple remotes etc... for ~$100. These can work great if you're willing to do the setup and testing.