A small portion of the "wood finish" on a picture frame/display case has peeled off- how can I repair it?

I have a large display case with a "wood finish," a tiny portion of which has peeled off, leaving a very small amount of whatever material the frame is made of (looks like black plastic) peeking through an otherwise wood-looking frame. I would like to touch up that tiny area...but without making things... show more I have a large display case with a "wood finish," a tiny portion of which has peeled off, leaving a very small amount of whatever material the frame is made of (looks like black plastic) peeking through an otherwise wood-looking frame. I would like to touch up that tiny area...but without making things worse. Thanks in advance for suggestions!
Update: I have a large display case (technically a shadow box) with a "wood finish," a tiny portion of which has peeled off, leaving a very small amount of whatever material the frame is made of peeking through an otherwise wood-looking frame. The material underneath is solid black and appears to be plastic. I... show more I have a large display case (technically a shadow box) with a "wood finish," a tiny portion of which has peeled off, leaving a very small amount of whatever material the frame is made of peeking through an otherwise wood-looking frame. The material underneath is solid black and appears to be plastic. I would like to touch up that tiny area...but without making things worse. Thanks in advance for suggestions!
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