if you are looking for the third gym badge i suggest Veilstone city.
it's the 3rd badge!
I have Pokemon platinum the 3rd gym leader always their your probaly just not lucky.
Hearthome's badge
in the 1st gym badge
you get the coal badge after defeating Roark in eterna city
The third Gym is the Gym in Veilstone City. You can get there by looking on your map. The leader specializes in Fighting Pokemon.
You can get a badge and TM Shadow Claw after beating the third available gym leader, which is Fantina with the Relic Badge. (She uses Ghost types)
Get the first gym badge
The fifth gym leader in Pokemon platinum is crasher wake but you get the fourth badge.
You can use the GTS in Pokemon Platinum after you get the first gym badge from the Oreburgh City gym.
you must beat the eighth gym leader and he will give you the badge.
Once you obtain a badge it's permanently stored in the badge case.