The Mute button!!Just Kiddng.

.Chinas are intended to be trashy,but in the context of the mix,they do not cut as well as the brighter cymbals,such as the hat and crash, and I happen to think that that is a good thing.This really depends on what you're after.If you want to bring the cymbal up in the mix you have to locate it's fundamental note.You can do this with a spectrum analyzer,or you can just give a big boost to the midrange gain,tighten the Q,(narrow bell curve)and sweep through the frequencies on a parametric EQ until you hit the most dominant frequency(1khz might be a good starting point)once you get that to sound good to your' ear,move on to the harmonics of that frequency(hopefully those are multiples of the fundamental).Do the opposite and cut the frequency you want to get rid of if you want to lower that cymbal in the mix.
That being said,IMHO,this is not the correct approach for getting good sound,this is a repair job.It`s best not to make EQ adjustments for one aspect of the kit,unless it enhances the other aspects of the kit.You are not just playing the china cymbal afterall,are you.
The best approach is to use the right cymbal for the right arangement,and the right dynamic aproach,(i.e.hitting with the apropriate intensity,at the appropriate point in time).
My approach is to use as few mics as possible to obtain a phase coherent sound for the kit.I usually use a coincidental pair of pencil condensor mics as OHs for cymbals,or sometimes I use large diaphram condensors and the Gylnn Johns technique,sometimes I'll combine both approaches.Very seldom have I heard of someone spot micing the cymbals in the studio(with the exception of the hi-hat),but if you have enough mics, and enough channels you can do it,it's just one more thing you will have to manage in the mix.
Again it's best to start at the source,and use the right player,the right instrument,the right room,the right microphone and placement. If a sound isn't of the right balance you can do three things;
1)Make the sound source it self louder,or softer,darker or brighter.(Hit it harder or softer,move it closer or further,move the source on or off axis to the mic)
2)Move the microphone to get that sound louder,or softer,darker or brighter.
3)Record in an environment that enhaces,or detracts that aspect of the kit.
Whenever you eq any mic channel on a drum kit,it will have a subtle effect on other parts of the kit,because if you are going to unmute it at any point where the other parts of the kit are being hit or are still ringing,that channel being turned on ,and off can have an effect on the sound of the rest of the kit,the shorter the duration of the fade in and out,the more noticable it will be,depending on it's level in the mix.
Don`t go into a session with preconceived notions of what cymbals or drum you are going to use.I`ve seen tracks ruined because the drummer insisted on using a splash cymbal that stuck out like a sore thumb.keep an open mind,and listen to your recording team.If you are recording by yourself,be your own biggest fan,and your`own worst critic.In other words,experiment!!
Hope this helps,
Rick