Been riding on indoor trainer recently and my very understanding neighbor below me says that they are now starting to hear the noise more and more. I have a few exercise mats down but that doesn’t seem to do the trick. Any other suggestions- blankets under the mat, foam insulation board, etc. Anything work?
I would add a few subwoofers and some good house music - they wont complain a lick about the trainer.
Only thing I have ever really seen quiet them down is one of them goofy trainer tires that are smooth. I swear I can hear the tread of my tire on my rear mount Cyclops, but not at all on my Kritler rollers…the rollers are pretty darn quiet.
I would guess it’s more from vibration than sound. I’d worry less about the
sound and more about how to isolate vibrations from the trainer to the floor
below.
Maybe a layer of bubble wrap. 
-Jot
What about rubber mats that are used in horse stalls? I think they would be thicker than exercise mats, and you can probably get them at a decent price at a farmers supply. I’ve never used them or shopped for them (so I may be way off base), but it might be worth while to look into.
Standard Marine Corps ISO mat works wonders.
Try a small 5x7 carpet and a thick carpet pad underneath as well. The two layers help decouple the vibrations better.
Dynomatting.
Get a piece of plywood cut large enough to fit the trainer and to both sides glue cheap carpet. Use a floor mat as the base layer, then take some old inner tubes that you’ve patched and partially fill them with air all to the same psi. Lay the carpet covered plywood on top of them then set your trainer up on this. You’ll need to play with the tube layout to get it even and stable and probably need to use a higher lift on the front wheel but the sound of silence will be worth it.
I just received a contitnental Trainer tire in the mail today. It purports to significantly cut down on noise. To my knowledge, only two manufacturers: Tacx and Continental – make such tires. I have not yet had a chance to install it though, so I’m not sure if it will work.
You could try finding some cork and plywood to build a “sub-floor” to train on. Cork is sometimes used underneath offices and other second floor spaces when there are multiple tenants within a building.
Bottom line…depending on your setup the builder did not care about sound attenuition when building and selling. You can help mitigate the noise, but you will never make it go away.
Perhaps you can buy your neighbor a pair of Bose noise canceling headphones 
If you want the best, and want to support a bike racing sponsor, go with Mapei products.
I work for a consulting engineering firm (building services) and we have some pretty clever acoustic engineers. Not only do they appear to understand acoustics, they can read chicken bones and even tea leaves. I think some of them can even communicate with the dead! (acoustics is a very black art to say the least)
They recommend and specify a whole raft of Mapei products for reducing (they won’t put their balls on the line and say eliminate) noise transmission in apartments and other similar situations. This consists of mainly acoustic (rubber) matting, of specific densities, under the flooring to prevent noise and vibration transmission.
Call Mapei and see what you can get as a sample? to fit under your bike trainer. ONce noise and vibration gets into a floor it’s very difficult to deal with. You are right to try and deal with the problem at the source and are a good neighbour for doing you best to deal with the problem.
A few people have hit on the main issue. It’s probably not the actual sound of the trainer, but the vibration running through the floor and joists and turning their ceiling into the speaker. Unless the structure was originally built to isolate the floors then you will have a hard time eliminating the vibration. I have tried everything I know to do and my final solution was to move my trainer to the garage.
The platform on tubes sounds like an interesting idea although I don’t know how stable it would be. The other issue with a platform is that it Could end up acting as an echo chamber. I was tempted to build a platform on industrial load isolators (basically like urethane bushings) but in the interest of a peaceful household, I made a workshop/trainer ridin’ area on my side of the garage.
I just received a contitnental Trainer tire in the mail today. It purports to significantly cut down on noise.
It certainly did for me! Tremendously so.
I’m using a $3.99 pool noodle cut to fit the feet of my trainer. It works well to dramatically dampen the vibrations that were transmitted through the floor (which was also our downstairs neighbor’s ceiling) due to chain vibration and the very slightly imperfect balance of the flywheel. I think it probably also isolates any shifting clunks. For better or worse, the noodles also provide a little cushioning action, but the one I used is very firm and doesn’t crush down.