I think a humidifier in their room helps a lot. If you get one that also removes impurities from the air as well as putting moisture into the air they breathe, it tends to calm the cough

Lots of rest (all ages)
Steam (all ages)
Saline drops and bulb syringes (all ages)
Extra fluids (all ages)
Warm liquids and chicken soup (6 months and up)
Elevating the head (12 months and up)
Humifier with Eucalyptus oil (all ages)
Eureka ointment on foot soles (all ages)
Honey (12 months and up)
Nose blowing (age 2 and up)

Yes a warm bath in a steamy bathroom is good!

Make sure their room is warm and the air isn’t dry. If you use a humidifier, put a couple of drops of eucalyptus oil into it.

get bub into the shower to decongest with the steam

Prospan is a trusted natural cough mixture for infants and children. It’s great. Available at chemists everywhere.

I find a water vaporiser helps my son when he has a cough.

I was told to cut up and onion on a plate and leave it in the room overnight, helps to reduce, if not stop, the severity of the cough. Remember to air out the room the next day. Hope this helps.

Lots of rest, a warm bath in a steamy bathroom, Vapor rubs and up the fluids.

Over the years I tried many cough mixtures but got the best results from as you are already doing, Vicks on bubs feet and as they get older Vicks rubbed into the back and chest gave me the best results for that horrible night cough.

For my kids i find keeping the chill out of the air but if using a heater make sure there is a bowl of water in the room to make sure the air isnt to dry(old wife tale not to sure if it works but it does for me). and using a bit of vicks on the chest, back and feet then cover foot with socks helps. if its a bubs under 1 use baby vicks. Not exactly natural but there is no need to take anything. And also if going outside even on a warmish day put a vest on to covet the kids chest.

Have a nice hot shower with the windows closed and the extractor fan off. The steam will help loosen up the mucous and nasty stuff on bub’s chest and upper respiratory system making it easier to bring up. You can sit in there with bub (take a chair to keep comfortable and off the cold tiles) and lay bub across your knees, face down then gently but firmly pat up and down bub’s back, the vibrations will help dislodge the nasty stuff. Just keep in mind that you will need to keep bub’s fluid up as the steam will make them perspire.

You can also steep lemon (skin and all) with honey in boiled water, it will help ease an irritated throat and congestion just make sure it is warm not hot.

Not sure how old your child is, but for myself and older children I find a teaspoon of apple cider vinegar in a cup of water can really help with a dry scratchy cough and has the added benefit of vitamin c in it.

Breastfeeding if you are able. Very good for immune system. Elevate where possible so any mucus doesnt sit on chest.