Only with the DM's permission can a PC directly create instantaneously a dead magic area… and that requires creating a new demiplane
The 9th-level shaper power genesis [metacreativity] (Expanded Psionics Handbook 109–10), in part, specifically says, "You can’t manipulate the time trait on your demiplane [that you've created by manifesting this power]; its time trait is as the Material Plane." This implies but—to be absolutely clear—does not state that when the shaper manifests the genesis power, she can manipulate the demiplane's other traits. Among a plane's—and, by extension, a demiplane's—traits are Magic Traits and among those magic traits is whether or not the plane is a dead-magic plane. (The Dungeon Master's Guide instead puts dead magic in its section on Planar Traits on Additional Traits (168).) (Also see this question.)
(By comparison, the 9th-level Sor/Wiz and Creation domain spell genesis [conj] (Epic Level Handbook 117) doesn't mention any planar traits at all. This reader remembers furious messageboard flame wars engaged in by supporters of all sides of the genesis spell, one side saying that the spell doesn't allow the caster to pick the demiplane's traits, another side saying that the caster can pick all the demiplane's traits including time traits, and a dozen other sides supporting every argument in between.)
Thus, so far as I'm aware, the the only guaranteed way that a PC can create an area of dead magic is this: The PC's player asks the DM if the player's PC can employ the genesis power or spell to create a new demiplane that possesses the trait dead magic, and the DM says yes.
Once that dead magic demiplane is created, the only magic elements that work there are any permanent portals like those described in the Forgotten Realms Campaign Setting (56) and Stronghold Builder's Guide (49–50). While it may go slightly against your vision of one level of the prison tower being a dead magic area, this is probably the safest way of securing prisoners in a dead magic area.
However, an antimagic area can be built into a stronghold,…
While not exactly the same thing, the sigils of antimagic (SB 83) (66,000 gp; stronghold) can cover one stronghold space (usually a room or roomlike section of a building) in antimagic (Dungeon Master's Guide 290). Effects that aren't affected by antimagic can be used when the stronghold's built in the space warded by the sigils so that, for example, the space is sectioned off by effects like walls of force or prismatic walls.
Creatures of greater than divine rank 0 can still use magic normally in the space warded by the sigils, and artifacts likewise function normally, so this may not be secure enough if the prisoner is friends with Blibdoolpoolp or Zuggtmoy or if the prisoner wears the head of Vecna.
…And the DM can just handwave the existence of a dead magic area
The Forgotten Realms Campaign Setting on Dead Magic, in part, says, "Dead magic zones often persist in places where extreme concentrations of magical power were abruptly scattered or destroyed—in the vicinity of a shattered mythal [n.b. Wikipedia has a mythal article?!], at the spot where an artifact was broken, or at the scene of a god's death" (56). So a group of enterprising clerics looking for just the right spot for their psionic prison might've happened upon just such an event in their research and opted to build at least part of their prison where such a momentous event occurred.
In the case of your prison, just make it so the momentous event occurred underground and the tower prison was built on top of it. For example, a clockwork elevator from the aboveground normal magic section of the prison could take guards, prisoners, and visitors to the undergound dead magic area of the prison.
