Wait was this comment because you don't know how special relativity works?

I know how it works, and indeed that was exactly the point of my comment You said that Hopefully in 160 years when someone leaves diamonds are still valuable and aren't all man made, which made it sound like you were referring to 160 years within the reference frame of the earth. To get to that diamond planet and back in 160 years "earth time", you'd need FTL travel. With your system, the question isn't so much if diamonds would all be man-made when the guys come back, but if there would be any humans left

ah yeah my bad, didn't even notice I said that. New plan. Move the earth. Take the reference frame with you and orbit said diamond planet.

Doesn't earth already have a ton of diamonds, but corporate greed (De Beers) puts a throttle on their selling and jacks up their prices to make them seem more "rare"? Albeit I'm not 100% certain of their quality...

There is a huge amount of diamond on earth. The problem is the vast majority of it is 'industrial' grade. Poor clarity, bad colour, small and irregular in shape, and contaminated with impurities. There is a huge difference between a 2 carat brilliant cut diamond, and 2 carats of industrial grade diamond bound for use as diamond dust. One makes impressive stones set in jewelry, the other can be used to make tools to make impressive things.

Isn't the value of diamond based on it's (or supposed) rarity? Surely mining and dragging the whole thing back to earth would provide an abundance of diamond, thereby reducing it's value? It would probably cost more money to make the trip, than profit you would generate from it.

The vast cost of retrieving anything from the diamond planet planet would likely be factored into the sale price and probably make anything harvested completely unaffordable by anyone resulting in no actual sales. Fortunately you can always try for plan B which is to find a way to refine the whole thing into a giant lens to focus some kind of solar death ray. Becoming supreme overlord would have more advantages over just the money from diamond sales in that the discounts you'd get on stuff would be better and you also pay lower taxes.

Then again 1g acceleration is kind of slow since humans can endure 4g.

Correction:
"Then again 1g acceleration is kind of slow since humans can briefly endure 4g."

No human has yet endured 5 hours at 4g, let alone a single day, week, month, or year.