"Is there an easy way to replace the stud?"

Remove the old piece, install a new stud.

I'm assuming the stud broke off flush with the head. If you're very careful, and very lucky, you can back the remaining piece outta the head by tapping it counterclockwise using a small, sharp punch and a hammer.

Otherwise you can try drilling into it and using a screw extractor ("easy out"). These come in two flavors: One looks sorta like a tapered reverse direction drill bit. The other is stubby, tapered, has sharp helical splines and ALSO has a shoulder -- this is my favorite and works better than the first type.

You can also find a left-handed drill bit and drill into the stud. Often the drill will catch and spin the piece out.

You can probably substitute an ordinary bolt 'til you can get the right stud (I'd steal one from a old motor). Otherwise buy a metric bolt at True Value as a short-term remedy.

If you have no choice, you can probably run your car without that stud for a short time -- but I'd leave the cap on and torque the remaining nut to retain the oil flow characteristics across all the cam bearings.

Buy two studs and replace 'em both. The remaining stud might take some unnecessary flexing.