I want my curves (fit by nonlinear regression) to be behind the data points, rather than in front of them.

Two issues are relevant here.

• Open symbols can be clear or filled with white (or background color). Sounds like yours are clear now. Easy to fill white, which is probably what you want to do. That is a choice in the color selector on the Format Symbols dialog.
• Prism 4 also lets you decide which data sets are in front of others. When graphing curve fits, the curves are (to the Prism graph) just another data set. The second tab on the Format Symbols dialog lets you reorder the data set. Note that you can click one button to reverse the current back-to-front order.