Where can I get the Challenger (normal human tank) in Saints Row IV?
I did this on the Xbox earlier today. Does not require cheats, mods, special inputs, or beating the main story.
Start an on-foot Mayhem activity (like the one where you use the black-hole gun).
Stay on the road the activity's start-point is found on and wait for a tank to show up.
Fire a black-hole near it, but not close enough to destroy it, just to deal a bit of damage; just on the edge of the black-hole's suction or blast radius. This will kill the driver and disable the tank.
Once disabled, quit the activity, rush to the tank, hop in, and scan it.
Bam! You now have the Challenger.
NOTE: This may take a couple tries to get it right, but it does work, even if you completed the activity before attempting to get the tank. Took me three tries to get it, since the first time it got blown up by a friend, but we found a Bear APC and tested the trick with that -- it worked flawlessly -- and second time it spawned on the road behind the start-point, so after exiting the activity, it had already disappeared before I could reach it.
To get this vehicle in Saints Row IV, start a Co-op Cat and Mouse and store it once you have control.
Source: Saints Row Wiki, "Challenger - Trivia" article
Also, the Enter the Dominatrix DLC introduces a new tank, the Dildozer. It is a human tank (kinda) similar to the Challenger. It will appear in your garage once you have finished the DLC missions.
Mods
Random Encounters Mod
Like its name suggests, this mod adds random encounters in the game where you will get attacked by different types of enemies (riding different types of vehicles) at random intervals.
It could spawn enemies that come riding in a Challenger tank (along with other vehicles rarely spawned or not spawned at all [some are SR3 vehicles] by the vanilla game). The tanks can be saved to your virtual garage (default key: N) while driving one.
Screenshots of the Challenger tanks that came with a random encounter caused by this mod:
(click on thumbnails to enlarge)
NPC Behaviour and Spawn Mod
One of this mod's changes are notoriety spawns. At level 3 notoriety, soldiers riding Challenger tanks will begin attacking with this mod.
Note: Some of this mod's files are the same as the Random Encounters Mod. If you want to use them together, either merge those files (instructions here) or overwrite Random Encounters Mod's files with this mod's files.
Additional Cheats mod
OP commented that he doesn't prefer modded cheats, but I'll add this for others willing to use modded cheats and for answer completion. This is probably the easiest way to get a Challenger tank in SR4. Description:
This mod adds 160 new cheats to the game, as well as changing all cheats to non-flagging... That means using them will no longer disable your autosave or achievements.
This mods adds a givechallenger cheat which will add a Challenger tank to your garage.