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 Monday, 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

Monday

Time Location Trainer
Morning
4am-10am
Johto - National Park School Kid Jack
Teams

First Battle
School Kid
Jack
Oddish Voltorb
Level 12 Level 14
Second Battle
School Kid
Jack
Gloom Voltorb
Level 29 Level 17
Third Battle
School Kid
Jack
Vileplume Electrode
Level 38 Level 31
Fourth Battle
School Kid
Jack
Electrode Vileplume Arcanine
Level 43 Level 52 Level 52
Morning
4am-10am
Johto - Route 43 PokéManiac Brent
Teams

First Battle
PokéManiac Brent Nidorina Nidorino
Level 20 Level 24
Second Battle
PokéManiac Brent Nidorina Nidorino Gyarados
Level 32 Level 34 Level 32
Third Battle
PokéManiac Brent Gyarados Lickitung Nidorina Nidorino
Level 41 Level 38 Level 38 Level 43
Fourth Battle
PokéManiac Brent Gyarados Lickitung Nidoqueen Nidoking
Level 48 Level 40 Level 58 Level 58
Morning
4am-10am
Kanto - Route 17 Biker Aiden
Teams

First Battle
Biker Aiden Tentacruel
Level 45
Second Battle
Biker Aiden Hypno Tentacruel
Level 50 Level 49
Third Battle
Biker Aiden Hypno Tentacruel
Level 55 Level 55
Fourth Battle
Biker Aiden Tentacruel Hypno Tentacruel
Level 55 Level 58 Level 58
Day
10am-8pm
Johto - Route 30 Youngster Joey
Teams

First Battle
Youngster Joey Rattata
Level 4
Second Battle
Youngster Joey Raticate
Level 34
Third Battle
Youngster Joey Raticate
Level 40
Fourth Battle
Youngster Joey Raticate
Level 54
Day
10am-8pm
Johto - Route 35 Firebreather Walt
Teams

First Battle
Firebreather
Walt
Magmar Magmar
Level 11 Level 16
Second Battle
Firebreather
Walt
Magmar Magmar
Level 25 Level 32
Third Battle
Firebreather
Walt
Magmar Magmar
Level 34 Level 37
Fourth Battle
Firebreather
Walt
Magby Magmar Magmortar
Level 26 Level 49 Level 58
Night
8pm-5am
Kanto - Route 13 Camper Tanner
Teams

First Battle
Camper Tanner Sudowoodo
Level 38
Second Battle
Camper Tanner Sudowoodo Chinchou
Level 41 Level 41
Third Battle
Camper Tanner Sudowoodo Lanturn Skiploom
Level 48 Level 47 Level 44
Fourth Battle
Camper Tanner Sudowoodo Jumpluff Lanturn
Level 52 Level 52 Level 52