In previous games, to get rematches with trainers, you used the VS Seeker to see if the trainers were willing to battle. In HeartGold & SoulSilver however, the rematches are done a different way. Firstly, only a few dozen trainers in Kanto & Johto are capable of being battled again.

In order to get the rematch, you have to receive the PokéGear number from the trainer in question. Then, on a certain day, you will need to ring the trainer in question to organise a rematch. It is not guaranteed that a rematch will be discussed when you call but keep trying and you should get it. Below is a list of all the trainers, battleable on Sunday, and their teams including their first team and each team's increase in level. Click the other days to go to their page

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday

Sunday

Time Location Trainer
Morning
4am-10am
Johto - National Park Lass Krise
Teams

First Battle
Lass Krise Oddish Cubone
Level 14 Level 17
Second Battle
Lass Krise Oddish Cubone
Level 21 Level 31
Third Battle
Lass Krise Gloom Marowak
Level 32 Level 38
Fourth Battle
Lass Krise Vileplume Marowak
Level 53 Level 54
Morning
4am-10am
Kanto - Route 27 Ace Trainer Reena
Teams

First Battle
Ace Trainer Reena Growlithe Nidorina Staryu
Level 36 Level 33 Level 36
Second Battle
Ace Trainer Reena Growlithe Nidorina Staryu
Level 38 Level 36 Level 38
Third Battle
Ace Trainer Reena Arcanine Nidoqueen Starmie
Level 47 Level 43 Level 47
Fourth Battle
Ace Trainer Reena Arcanine Nidoqueen Starmie
Level 54 Level 53 Level 56
Day
10am-8pm
Johto - Route 34 Picnicker Gina
Teams

First Battle
Picnicker Gina Hoppip Hoppip Bulbasaur
Level 9 Level 9 Level 12
Second Battle
Picnicker Gina Hoppip Hoppip Ivysaur
Level 24 Level 24 Level 32
Third Battle
Picnicker Gina Skiploom Skiploom Ivysaur
Level 26 Level 26 Level 44
Fourth Battle
Picnicker Gina Skiploom Jumpluff Venusaur
Level 30 Level 36 Level 55
Day
10am-8pm
Johto - Route 42 Fisherman Tully
Teams

First Battle
Fisherman Tully Qwilfish
Level 19
Second Battle
Fisherman Tully Qwilfish
Level 33
Third Battle
Fisherman Tully Goldeen Goldeen Qwilfish
Level 30 Level 30 Level 38
Fourth Battle
Fisherman Tully Seaking Seaking Qwilfish
Level 41 Level 50 Level 53
Day
10am-8pm
Kanto - Route 17 Biker Ernest
Teams

First Battle
Biker Ernest Teddiursa Marill
Level 45 Level 44
Second Battle
Biker Ernest Teddiursa Azumarill
Level 46 Level 47
Third Battle
Biker Ernest Teddiursa Azumarill
Level 48 Level 49
Fourth Battle
Biker Ernest Ursaring Azumarill
Level 58 Level 54
Night
8pm-5am
Kanto - Route 17 Biker Reese
Teams

First Battle
Biker Reese Weezing
Level 45
Second Battle
Biker Reese Arbok Weezing
Level 42 Level 48
Third Battle
Biker Reese Arbok Weezing
Level 48 Level 50
Fourth Battle
Biker Reese Arbok Weezing
Level 56 Level 55