Pulse cranberries and orange in a processor until finely chopped but still textured. Stir in sugar and refrigerate for 30 minutes, then drain in a fine sieve for 5 minutes without pressing into a puree.

Split mini rye rolls horizontally. Spread cream cheese in a thin, even layer over their cut faces.

Divide the turkey into 24 equal portions. Tuck one dry lettuce leaf into each bottom and fold one portion of turkey over it.

Divide the drained relish over the turkey in a shallow layer and close the rolls. Wipe away any filling that spills beyond the bread.

Yield 24 whole mini sandwiches, two per serving. Refrigerate in a covered shallow container and serve within 8 hours of assembly.