Not easily. Density is the ratio of air mass to volume, and volume is inversely proportional to pressure.
If you increased the pressure, that would have side effects on living organisms; modifying the temperature would have similarly undesirable effects in a very short time.
Supposing the gravity gradient was reasonably flat, changes in gravity would affect density, but they'd also affect whatever needed to be buoyed so as to neutralize any benefit.
One way to go might be to introduce some kind of unobtainium gas, with the following properties:
- not reactive, or very little (except maybe in circumstances which could add to the story? - a little like the miglign lifting gas of The Wooden Spaceships by Bob Shaw, even if that's set in a different Universe with different physical laws).
- very dense
- transparent to visible wavelengths
What would this entail? You would get more buoyancy, at the expense of lowered partial pressure of oxygen, so the air would be less breathable. You'd need to proportionately increase the oxygen content of the air.
The gas, being dense and hence quite heavy, would tend to pool in lowlands, so that digging e.g. a well would become very difficult unless ventilation was provided; any hole in the ground would become a death trap in still air.
Even with reasonable recirculation, the gas distribution would not be linear; you would get a sort of layer - say two hundred meters thick? - of "heavy air" where you get high buoyancy, then the air would revert quickly to normal; the airships would "float" on an ocean of heavy air, much as seaships float on an ocean of water. You'd get interesting optic effects too, if the gas' refraction index was sufficiently different from that of normal air. In the right circumstances, you could "see" over a hill by looking at the "sky" immediately above it.
With time - a very long time - you'd also get parapatric speciation, and have heavy-air creatures better adapted to life in the lowlands, and light-air creatures adapted to live on the hills. Speciation would be slow to come by since the differences between the two habitats would be small.
There would also be other effects due to e.g. changed convection parameters - depending on the gaseous unobtainium thermal dilation and capacity, it could be too easy, or very difficult, to get good airflow out of a chimney in the lowlands.
There might also be some other effect I have overlooked and which could nonetheless make this whole exercise pointless, because it would interfere with life or civilization in some way.