Scarlet-Tech
Could you take video or audio recordings and link them by posting it to youtube?  
 

I tried doing this once, but for whatever reason, my attempt to capture it captured the sound of my keyboard as I was playing Minecraft, but not the coil whine. I was a bit surprised since the coil whine noise isn't really that high pitched or minor and is more apparent than that (and two other people I've asked about it could hear it as well, one who supposedly has lesser hearing, so it's not just me hearing things).
 

Scarlet-Tech
What would your options be for upgrading away from the 970?  is there a possibility of maybe selling it and getting a 780ti or a 980?  I know both will cost more money out of pocket, but it may give you some relief from the coil whine itself.

Honestly, I don't know. I'm really frustrated from it not only because of it, but because of everything else. Here's a little back story (I attempted to use a spoiler tag on it because it's long, but it didn't seem to work, so sorry).
 
About a year ago, I upgraded my desk, which meant a smaller case, which meant I needed a new PSU. The case is a Fractal Arc Midi, and the PC Power & Cooling Silencer 610, much as I'd love to have stuck with it, wasn't working. The CPU auxiliary cable wouldn't reach without routing over the graphics card, and though there were physically enough SATA connectors, not all reached either. So, I did some research, and found out the EVGA SuperNova G2 was a fantastic Super Flower unit, and got this over a SeaSonic unit I was originally going to get. I got it and loved it, though it had a very minor noise like coil whine, but I want to stress the very minor part. I can only hear this noise if the PC is off (no fans running), the PSU is on, and my head is directly next to the case by the PSU, and even then it's minor. That is an example of coil whine that exists but is a non-issue to me. I asked about it anyway, and was told it's not a fault or something I should be concerned with. So, I was happy with my "new" PC.
 

 
Later (late August or early September), my EVGA GeForce GTX 560 Ti started having issues. It would freeze, essentially. I first noticed it one night after I cleaned some dust from my side panel fan. I shut the PC down, took the side panel off, cleaned it, and put it back on. After that, the card was misbehaving. Beforehand, it was fine. The symptom was that after about fifteen seconds to two minutes of playing a game (first noticed in Aura Kingdom, an undemanding MMO), a portion of the screen would sort of flicker, and a second later, the video and sound would just freeze. I later tried Minecraft to see if it was the game and Minecraft did about the same. I tried changing drivers to no avail. I tried the onboard iGPU and an EVGA GeForce GT 430 from my media PC and both worked fine, so I figured the graphics card finally died. Here's the odd thing; it did this at ~56C, so it wasn't overheating. It had to do with being put under a sizable load. I had issues with it freezing around 86C right when I first got it (namely with Crysis), but then they went away (or maybe it seemed like it because I played Crysis less and more Sims 3 and Minecraft), so I thought nothing of it. I also had a lot of these...
 

 
...throughout the life of the card, but reinstalling drivers usually fixed it. Maybe it was borderline bad all along? I don't know, but I digress. I want to note that I took it apart and noticed a very, very minor burn mark near one of the smaller VRM (I think that's what they are) chips.
 

 
I do not believe the PSU to have caused it though, and I do not blame it for the coil whine with the GeForce GTX 970s since the same thing happens with another PSU anyway.
 
Given this was around later August or early September, and I was planning on an upgrade soon, I figured I'd wait and see on the rumors of supposedly new nVidia GPUs coming. They did get announced, but availability was low, and I needed something in the interim, so I got a PNY GeForce GTX 650 for ~$60 from Best Buy, which was actually a good deal (this thing seldom knows what 60C is and runs insanely quiet, by the way). I was originally going to pass the GeForce GTX 560 Ti to my nephew, so I figured this wasn't a waste as I could do the same with it later.
 
Anyway, I finally got my GeForce GTX 970 ordered early November. It's now going on three months later, and even longer since I've been without a good GPU. My frustration is growing (I guess it would be over that point by now but I try not to let it get the best of me).
 
I don't know what I want to do. This GeForce GTX 650, as quiet and cool running as it is, with performance that surprises me for such a small chip, won't do for my long term desire. I don't want a GeForce GTX 980 (too pricey for too small an increase over a GeForce GTX 970), and I'm not a fan of buying used GPUs. I imagine the GeForce GTX 960 is an option (if I want to consider nVidia, that is), but I was hoping for more performance than that. It's a shame because the GeForce GTX 970 is seemingly otherwise perfect, but I haven't even gotten to really experience it (and I don't even know if the whole VRAM issue would impact me, but that's another thing that still stains nVidia's reputation for me).

claytonma
I sold this card btw. Worst gpu purchase in history for me.

As someone who feels the same, what did you end up doing? I feel like I am going to need to do the same and sell it, unfortunately. The current courses of action are set to keep me stuck in an endless loop, I feel.