You will see many backyard rinks with painted lines.  Some are well below the ice surface and some are painted on top and resurfaced over it.

I have not done this as of yet and am not so sure I want to.  Everything I have read says that lines can cause the ice to melt prematurely.  Given that piece of information you really need to think twice about doing this before you do.  The people @ Nicerink (http://www.nicerink.com/) have quarts of paint in an array of colors that you can get.  If your rink doesn't get too deep you can probably just paint your liner, wait for it to dry and flood the rink.  Otherwise you will be painting on the ice and resurfacing over it a few times to set it in.

I read somewhere that someone used red and blue duct tape and taped the lines to the liner. The reported that the tape was under enough ice that they were visible, but didn't attract the sun the way lines painted close to the surface will.  This seems like a reasonable idea, but as I haven't tried it I cannot say it is accurate.