For trumpet, I concur with the previous response, and will add the first movement of Greg Bartholomew's Summer Suite. The movement is called Popsicle Rocket Sunrise and technically is very playable.

for Tuba:
Concertpiece No.1 - Vaughan
Ricercar - Gabrielli/Morris
Variations on a Theme of Judas Maccabeus - Beethoven/Bell (just moved back to class 1)

If your student can play a high D above the staff, then Lento by Holmes could be a good choice.

Finally, if all of those prove to be too much, these Class 2 solos can provide a good challenge:

Largo and Presto - Marcello
Larghetto and Allegro - Handel/Little
Colossus - Vandercook

The first two of those used to be on the Class 1 list.