Sorry, I don't know what specific type of connection those are, but maybe I can help.
You're already using DigiKey, that's usually my first stop.
If you don't already own one, get a
digital caliper like this one. I'd recommend just getting the exact one I linked, the reviews say that it's accurate (very important).
I just looked up any random connector on DigiKey as an example. Almost everything on DigiKey has a link to the datasheet in the description. Take this one for example...
http://www.jst-mfg.com/product/pdf/eng/ePH.pdf
Scroll down and you'll see that it gives precise measurements for it. You can use the caliper to measure out the connector on the NES board and compare, that way you wont just be guessing. This is why a
digital caliper is essential, otherwise you might find it impossible to measure in mm and be accurate. It may take some time to find the right one, but it's not impossible (unless the connector is proprietary or no longer made).
If you're able to find the right one, be sure to post what it is!
edit: I'll also say that, if you can't find a connector that'll fit, all isn't lost. I'm assuming you need to replace the female plug because it was damaged or something that'll it'll otherwise no longer work. If you can't find the correct plug, there's ways around it, although soldering is required.