The darker side of BH is doing whatever it takes to control and funnel wealth. Any site can be taken down (at least temporarily and often permanently) or messed with to a point that the owner simply gives up. It's been done, it's being done - and if you don't believe it, so much the better for the people that are capable of it.
I'm not talking about childish dos attacks, I'm talking about getting the website owner banned from each and every money making effort he has, losing his credibility, and losing his hosting. It's not very nice maybe, but it CAN be done with the right techniques.
The OP here DOES NOT want to resort to this level of play. He simply wants to make his competitor a little less of a threat. Unfortunately, he's forgetting the very small problem of order. If THIS competitor isn't in spot 2 and spot 3 -- someone else WILL be.
Solution, rank in spots 1, 2, and 3. If you got to 1, use the same techniques to truly dominate this area. If you don't want to be malicious, be better. Decide what measures you are willing to take - and take them as far as you can.
Find out more of what they are doing. Maybe they are spamming and stuffing keywords a little or using other techniques the google frowns upon - and you dropping a legitimate note off to google could solve your problems. Where are their links coming from, maybe you can see a pattern the bots can not. If you don't know what Google frowns upon, look it up here:
Code:
http://www.google.com/support/webmasters/
Take an in depth look at their site, figure out why people are passing you to go to their site, and make your site better. Do a review of your site on your site so you can get an indented listing to make a little more space between your site and theirs.
If you eliminate this competition, will your traffic still leak to the new number 2 and number 3 spot? Find the problem. Once they are on your site ----- they SHOULD NOT leave to spend their time/money somewhere else. They should be satisfied, or at least made you some money.
Too Soon
... anyway, shafty and I share the same views, and I've had experience with this too. I confirm what he's saying. You cannot influence things in which legit ranking and established sites are easily deindexed. I said it's not easy, meaning you can't accomplish it, no offense, but if you can match and excede your efforts in numbers then theorically it SHOULD be possible, that I don't know. My own experience confirms Shafty's.