The most obvious solution is to set both Color Temperature and White Balance Correction manually.
CT adjusts along an amber←→blue axis.
WB adjusts along a magenta←→green axis.
The two axes are roughly orthogonal to the other.
Will you get it exactly the way you want it on your first try? Almost certainly not. But you need to start somewhere if you ever want to learn how you can tell the camera how you want a certain photo to look, instead of leaving it the other way around!
The best way to learn how adjusting CT and WB affect the colors in an image is to save your images in raw format, which is .NEF for Nikon cameras, and then play with the controls in your preferred raw convertor application.
As to keeping the green tint caused by green plants, you likely want to leave the magenta←→green adjustment at the neutral point. Your camera is applying a few ticks towards magenta.
From personal experience shooting a lot of high school field sports, I can confirm that I must use a significant amount of correction towards magenta to control the "greenish" skin tones on the legs of the athletes due to the light reflected up from the green grass. I then use the HSL tool (see below) to pull back magenta a little so that their faces, which are nowhere near as close to the grass and thus not getting as much reflected green light, don't get too pink. Under artificial lighting at night, the magenta adjustment in the HSL tool (along with reducing purple and even a little blue and red) also helps to eliminate the color cast from white jerseys, which are almost always made from synthetic fibers that "glow" under typical stadium lights. The camera sees this "glow" much more than our eyes do.
Here are a few links to existing questions and answers here at Photography SE to get you started:
What is color temperature and how does it affect my photography?
What is white balance in a camera? When and where should I use WB?
How do I find the right white balance value to set in my camera?
Why are high white balance temperatures redder when warmer objects are bluer?
Once you've gotten comfortable with CT and WB, you can then move on to learning how to use an HSL/HSB/HSV¹ (Hue-Saturation-Luminance/Brightness/Value) tool to fine tune specific color bands² around the color wheel.
1 You don't have to abuse the HSL tool to the point of eliminating all but one color as the examples in that link show in order to demonstrate the sheer power of the tool. Here is a question with another example of what the HSL/HAB/HSV tools can do.
2 The example at this link is much more subtle, yet shows just how much a few HSL adjustments can do to make the image look closer to what one expects. It's particularly useful when shooting under poor, limited spectrum lighting.