I have oily eyelids (& oily t-zone) too. I'm using Missha M Super Black Brush Pen Liner.

I've tried many types of liner - pen, gel, liquid from various brands. I usually start applying makeup at around 7am before work and by 11am, i have really 'nice' very smokey under eye.

However, with Missha's, it stayed put even without any primer. The brush is soft and it's really black. It's actually very easy to apply, you just have to have your hand being steady when applying. At first I started with pencil liner but, it's just not good enough for me, then gel. But gel liners dried up so fast! And have to dip into the jar so many times... which i hate.

FInally tried liquid, easiest to use btw. Love it.

Maybe you can try to google that? I don't think they have here in KL. I've purchased mine direct from Seoul when I was there this year and also asked my sister to help me buy it when she was there last month.