How can one get the "Diamonds to you!" achievement in singleplayer? The achievement list cannot be completed without it. Perhaps it can be possible by passing a diamond to a zombie?
Yes, you can get the "Diamonds to you!" achievement in singleplayer. There are 2 ways to get it. The first is precisely what you describe; you can throw a diamond at a zombie, and if they pick it up, it counts for the achievement. Not all zombies will pick things up though, so you may need to try a couple zombies.
The other way you can earn this achievement for a singleplayer world is to open the world to LAN. This may not be possible if you don't have another player, but it is an alternative method if you do have someone else that can connect to your world over LAN.