- I am conscientous about the ability to maintain a consistently high standard of work under pressure.
- I am conscientous with the ability to maintain a consistently high standard of work under pressuer
In my view, neither sentence is correct. You are not conscientious about 'the ability', but about maintaining a high standard (etc). I would rephrase it to say: "I am conscientious, and can maintain ...".
If you want to use the second sentence, then I think it should read: "I am conscientious, and am able to maintain...".
Actually I thought that concepts like "conscientious" and categories one can be conscientious about should transcend the languages, as it should be similar, as long as the meaning of what "conscience" is, is also similar.
"I conscientiously maintain a high standard of work under pressure." is a correct sentence (I think). I prefer something more like "I am a conscientious worker who maintains high standards under pressure."