I might have spoken too hastily when I said the TR2-R1 won't fit. It will fit, but it makes contact with the 12V connector, and I don't like that. The Alpine 64 is clear, but just barely. Having just discovered this annoyance, I'm annoyed by it. But I will probably get used to it after a while.
Here is a cheap cooler that will do the job:
http://www.ewiz.com/detail.php?name=FAN-8ID2AL
eWiz has also several similar models in the same price range in case you want an alternative. The nice thing about that one (aside from the fact that it isn't much larger than a stock CPU cooler) is that the 80mm fan can easily be replaced if necessary.
This one is a step up, but it's actually a little bit louder:
http://www.ewiz.com/detail.php?name=FAN-9ID3A
I haven't used either of those in a while, and I can't remember if the automatic fan control works with their 3-pin connectors. If it does, then noise shouldn't be a problem.
By the way, I'm actually using an Alpine 7 without the LGA775 mounting hardware instead of an Alpine 64. (Aside from the mounting hardware, they're practically the same.) I have an older Alpine 64 that has a 3-pin connector and I don't know if the newer ones have a 4-pin connector; but the Alpine 7 has a 4-pin connector, so that's why I'm using it instead.
I don't have an Actic Cooling Freezer 64 Pro that I can try out with the GEFORCE6100PM-M2, but I have a Freezer 7 Pro (aside from the mounting hardware, they're practically the same), and just from eyeballing it, it looks like the Freezer 64 Pro would fit alright. So would a Mini Typhoon or a Big Typhoon, but those cost a lot more than $15.
I hope this helps.