You may remember me from "You'll never get that RGB color in CMYK!"
Now, you said you wanted something darker than Cyan70 +Yellow100:
You don't have much choice to darken your color and keep it bright, you need to add more Cyan! Try C75 + Y100 and keep adding your cyan until you are satisfied.
Forget about your RGB green, and work with the good old color system by adding your CMY values to keep your colors bright and mixing them as it's done with paint. Black will make them more dull so don't add any.
Cyan + Yellow = Green
Magenta + Cyan = Purple
Magenta + Yellow = Bright Red
And yes, your screen might not be perfectly calibrated, but even if it is, CMYK do look way "darker" than RGB colors. Trust your brain, if the Cyan + Yellow you choose to make your green looks like the best you can do, and if the suggestions for the Pantones are close, then these are the right (best) values.
Use a Pantone Chart if that can help you. It's better if you have a printed one, so maybe add this to your wish list! That will help you see some Pantones and their CMYK recipes and have an idea how it looks like on paper (coated or uncoated.)
From what I can see, the closest Pantones to your green is Pantones #360 and #361. You could also have a look at #376 if you want it more lime, it's a very nice bright green once printed.
Some real life examples close to the colors you can expect. It's better than you think.
Pantone #368 with (probably) Pantone blue 072 or Reflex Blue:
There's also Pantone #347 that is often used for logos and very pure green too.
Maybe this can interest you as well. Nice pictures with Pantones.
That's another good trick to start noticing prints you see everywhere
and that you know well, and then verify on the brand or logo guidelines
what are the colors used. You can often find these info on the brands' websites, developer or media sections, or sometimes Wikipedia. After a while, you will know instinctively
what are the best mixes or Pantones to use and you'll have your favorite