Gluing styrene tire halves together and achieving a long-lasting bond is no problem, if you're using a solvent-type liquid glue like Tenax or MEK.
The tendency of the "old" plastic tires to fall apart over the years was due to the old tube glues, which really did nothing to meld plastic parts together. Super glue is an improvement on tube glue, but it still works much the same way. Solvent types actually melt the styrene and intermix the molecules from both parts.