You can't trade these breeding tools and give others a shortcut. That ruins their quest for one of the high achievements in pokemon in-game play. The "Monotony Badge" is the unwritten final badge you have to earn in every pokemon game. Here's the battle order in the Monotony Gym (the gym leader is named Game Freak).
1) EV train any pokemon. Macho Brace and Pokerus help a ton, but it's still a huge tedium test to faint dozens of Zubats, one after another, just to get those damn 252 speed EV's.
2) Catch the roaming legendary dog in Kanto. Unless you're really lucky, you'll need all your boredom prevention moves for this one. Not only do you have to wander back and forth over and over, but you also can waste repels, ride through grass needlessly, and soft reset a bunch.
3) Breed for Nature, Gender, IV's, or all of the above. This tedium test has already been covered in this thread.
4) Berry farming. Not hard, but time-consuming. Plant, water, wait, water, wait, pick, repeat, repeat, repeat...
and the final championship fight in the quest for the Monotony Badge...
5) Catch a Feebas and evolve a Milotic in Emerald . This will be the ultimate test of your boredom battling skills. Zig-zagging methodically over every single square of a large body of water, fishing 3-5 times on each square, having to pay close attention to the damn dots on the screen so you can hook the poke at the precisely correct instant, repeat the process hundreds of times for hours and hours on end -- ah, now that's a fight! After that, you get to raise the Beauty of the damn thing, which probably requires a bunch of rare berries (see above). This task is truly the gold standard of mindless minutia.
What fun would it be to rob others of the joy of pursuing this coveted badge?