You need to distribute force over time
The difference between a punch and a shove is that a shove distributes the impact over time. With bullets, no matter what you make it out of, this is very limited. Even rubber bullets or bean bags would cause major trauma long before they shove a person back because you only really have a few millimeters of compression before the projectile become ridged enough to pernitrate the target.
Instead you need to transfer the force using a fluid. Water works very well as you see with a Fireman's hose, but they are not portable; so, what you really need is a very powerful water gun. The strongest commercially sold water guns in the world use CO2 cartages like you use in a paintball gun.
A typical paintball CO2 tank weighs about 24grams with a total potential energy of about 432J. Because a CO2 tanks loses efficiency as it decompresses and needs time to warm back up, the most sustained energy you can get out of a CO2 is about 1/4 of its total capacity over 5 seconds. IE: 20 J/sec.
It generally takes about 80 J/sec. to even start pushing a normal grown person backwards. So, lets say you want to push someone back 10 ft over the course of 10 seconds, using a CO2 powered water gun, you would need to increase your total potential energy up to about 7000J which would need to be stored in a series of CO2 tanks that are opened in sequence to levelize out to a sustained push as the CO2 tanks lose pressure and cool down. Water guns also suffer a lot of energy loss over distance; so, while a 7000J tank system may work at near point-blank ranges, you may need several times this for a longer ranged water cannon.
First, you will want a more efficient CO2 tank. A portable sized 3000 PSI fiberglass CO2 tank translates to about 80 Joules of potential energy per gram of weight after you account for inefficiencies like the weight of the tank itself and escaped gases, meaning you store the force required to push a person back 10ft from point-blank range with a set of CO2 tanks that weigh just 6lb. But, water guns are not super efficient over range; so, if you want to knock someone back from farther away like 10-20m, or someone who might weigh a bit more than average, I would expect you to need something more like a 20lbs of CO2 tanks at least.
The harder part would be the weight of the water. A high end CO2 water gun can fire 30oz of water per second (usually in burst of less than 1 second). The higher pressure CO2 tanks means you could achieve much more force per mass of water; so, to get 8 times the force of a normal CO2 water gun with 4 times the pressure, you need 60oz of water per second. So a 10 second burst would require 600oz of water (37.5lb).
So to give yourself a 10 second burst "portable fire hose" you would need about a 20lb CO2 tank, a 40lb water tank, and probably 5-10lb for the actual water gun, tubes, harness, etc. giving you a total weight of just around 65-70lb.
While this sounds unreasonably heavy, keep in mind that the M1 Flamethrower weighed about 70lb and could only fire for about 15 seconds; so, basically what you are making here is a non-lethal flamethrower. Also, the weight of the weapon system will help offset the significant recoil. Can't say if this would be practical enough for your setting, but it would get the job done.
It's also worth noting that getting hit with over half a gallon of high velocity water a second is still going to hurt quite a bit. Your target will likely sustain bruising anywhere the water hits him, and possibly break a few bones as he is knocked back and tumbles from the force of the spray... but it would be very unlikely to kill a healthy grown person; so, should still meet the qualifier of a "non-lethal" weapon.