It is a PITA, but GD has the best price - $7.05 with coupon: goxtgi200c so this is how I do it:
Check availability on another website. (such as Moniker, although they are a bit slow).
When I see one I want I go to Godaddy and type in 8 or 10 random letters in search. when it comes back available (surprise!) I click checkout, wade through the ads, log in, wade through more ads until I get to the cart page. I enter the coupon and click. Check to see that the coupon still cuts the price to $7.05. (this is important because if the coupon did not work then it would take time to find another one. The longer between the time you enter your real choice in the search box and when your order is finalized, the greater the chance that a front runner grabs it.)
Leaving the nonsense domain in the cart I then click Domains > Bulk register. (even if I have just one choice) This is because nameservers cannot be set beyond the first chosen domain and because yet another bug has disabled the unlock feature, at least on my domains, so I cannot change nameservers.
The Bulk Register avoids a lot of the junk and I arrive back at the cart rather quickly. Now I must remove the nonsense domain - very important! - and then check out normally.
A real question if all this (and dealing with SlowDaddy's terrible control pan el) is worth the 30 cents per year that I save over Moniker, but that is the system.
Three domains were snatched from me before I learned the above system, all three times I did a bit of extra research after I searched the name or put it in my cart, and went through checkout apparently successfully - only to receive a failure notice a few minutes later. And all three times GD got me the name a day or two later without any additional action on my part.