Is it possible to create negative ions without ionization?

An air ioniser (or negative ion generator or Chizhevsky's chandelier) is a device that uses high voltage to ionise (electrically charge) air molecules. Negative ions, or anions, are particles with one or more extra electrons, conferring a net negative charge to the particle. Cations are positive ions missing one or more electrons, resulting in a net positive charge. Some commercial air purifiers are designed to generate negative ions.

Matter consists of neutral atoms and molecules, there are as many electrons ( negative particles) as positive ( protons) in the universe is axiomatic because that is what has been observed, conservation of charge is inherent.

The way the air purifiers work is by separating the electron from the atoms/molecules and allowing it to attach (by the laws of quantum mechanics) to neutral atoms/molecules making negative ions. This means that the parent of the electron becomes positive, and in the single processor described above it is inevitable that there will also be positive ions.

One could create a beam of electrons of appropriate energy and negatively ionize the air. The charge balance would happen where the beam of electrons was formed, leaving positive ions in the region of generation. In total space, charge would add up to zero, but there can be a separation of charges.

If you are asking : "Can we create negative ions without creating positive ones?"

The answer is: No.

Whenever a neutral system is provoked to generate ions then equal amount of oppositely charged ions are created (always). This is simply the law of conservation of charge.