Found this in a Japanese site; hope it helps.
By the way, it reads: "korosarenakereba tsuyoku naru" (just in case).

I think others got the meaning wrong. This is what you say to someone when he/she is hesitant to take a risk. You're telling that person to go ahead and take the risk, see what happens, think positive! So a common Japanese saying for this is 当たって砕けろ (atatte kudakero)。This is how I would translate this phrase if I were translating a movie script. The Japanese audience would get it right away.

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Note added at 4 hrs 30 mins (2006-01-12 07:01:48 GMT)
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Hmmm, on more Googling, this saying is also used when urging someone to eat something that may be bad. In that case, there really wouldn't be a Japanese equivalent I can think of. (Do the Japanese ever encourage eating something that may be bad/strange? Do we need encouragement? Ha, ha...) Although I guess atatte kudakero could be a pun in very bad taste when you consider that atatte also means food poisoning and kudakeru is similar to kudasu, which means "the runs"....

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Note added at 4 hrs 39 mins (2006-01-12 07:10:35 GMT)
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OK, so it really depends on context. There also is an essay with this saying as the title, talking about the sufferings and struggles experienced during and in the aftermath of Hurricane Katrina. In that case, "これを生き延びれば、それだけ強くなる、てことだ" would be good.

The first part is a twist of "if it doesn't kill you", namely instead of being killed (which is a strange notion in Japanese cultural setting -- thereby no direct way to translate).
As you see, my translation is more common and fits to Japanese psyche.
Don't ask me the derivation. This is a product of a writer's instinct (being a professional, published author of six books).
Besides, momoka-san's quoted site is not a work of a professional.
Remember, everybody (without proper credential) can put out website.

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Note added at 13 hrs 27 mins (2006-01-12 15:58:48 GMT)
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艱難汝を玉にす
Little adjustment and this is my second suggestion -- which is far better as I have given more thoughts about this.
The conclusion (in part) I arrived is that this age-old cliche 艱難汝を玉にすwould be the most suitable.
Although this expression, in my thinking, is almost equivalent of Western favorite mode of thinking 適者生存 (Survival of the fittest -- essentially what this means is "if it doesn't kill you, it will make you stronger").

I just happened to come across the "unofficial but pretty good quality" Japanese translation of the song Stronger (What Doesn't Kill You) by Kelly Clarkson. There is a part in the lyrics that goes "What doesn't kill you makes you stronger...", and the Japanese translation says "人は傷つくと強くなるものなんだ". I only changed なんだ to なのだ to sound less casual, but I'm pretty sure this is a very good translation. After reading all the suggestions on the Internet, this made the most sense to me.