I had this exact problem and have tried many different papers, but my printed digi image always seemed to run slightly with the Copic markers....but just this week I found that the Wausau cardstock, Bright White, 65 lb, 96 Bright works great, no running at all! I got a small pack of it at Target and it works perfectly! I just print the digi stamp and then set it for a moment with the embossing heating tool and I can color right away with the Copic markers with no running at all. It's amazing!
Just a small side note, the Wausau 110 lb cardstock was on sale at Michael's so I got it just last night and it does not work, my printed digi image did run just slightly with the Copic markers on the 110 lb....so it seems only the Wausau cardstock, Bright White, 65 lb, 96 Bright works. I think if you try this exact paper it will work for you. Also, I do not have a laser printer, I print my digi images from a plain HP printer. I have tried the Georgia Pacific cardstock from Walmart, Bazzil and several other cardstock brands but they all ran the moment I used the Copic markers.
I wish you the best of luck. You might want to try the Wausau cardstock, Bright White, 65 lb, 96 Bright.
Best wishes, Becky