Stable colloidal dispersion of alumina in water is governed by particle size and nature of solvent. If the particles are nano then they will remain in the body of solvent. However if the particles are micro or semimicro or nanoparticles agglomerate then they settle at a very short notice as you mentioned in your question.
You can disperse Al2O3 in organic acid like citric acid or acetic acid followed by ultrasonic blending in an ultra-sonicator or probe sonicator. The stability of nanoparticles is also very good in the acid range of pH ~ 4.5 - 5. These organic acid acts as a capping ligands. You can also try to dissolve aluminium oxide in organic solvent such as ethylene glycol or isopropanol. After synthesis of nanoparticles, capping ligands can be removed by heating at high temperatures (approx.120 ºC to 150 ºC).