Here is what I come up with:
Assumed service voltage is 120/230 1ph 3-wire.
The main loads on the feeder are 230V loads which don't use the neutral conductor.
Per the NEC table, 75 deg C column, #8 THHN CU is rated for 50A.
The new feeder can be 2-#8 THHN hot conductors, 1-#10 THHN neutral, and...