I live in a townhouse and I can often hear my upstairs neighbours, although it seems only to be on the weekends, so it may be when they have guests or something.
Anyways, I think it would bug me a lot less (I have gotten somewhat used to it though) if they had approached us (my family) and let us know when they were going to be having a party or a large number of people over and it may be a bit noisy...
So, in that regard, I think your downstairs neighbours would probably appreciate if you just went and asked them when the most appropriate times to use the treadmill would be. Perhaps the baby goes out for a walk at 8am (good time to use the treadmill) or always has naps at 1pm (bad time to use the treadmill). I'm sure there would be numerous times though out the day that it would be appropriate.
But of course, you may not have to worry about this at all if they can't hear you (i.e. the carpet idea or asking other neighbours if they've had a similar problem).
Either way, it's awesome that you're being considerate of them, however, if it were me, I would just get the treadmill and do my best to try to avoid my neighbours (just kidding

). But I would get the treadmill and just try not to make too much noise on it.