What is the dosage of Ambroxol for Rats by weight?

Analogous to the dosage for Human children, adding a bit more to compensate for rat’s quicker metabolism, the dosage for rats is 0.5 to 1 mg/kg BID.  See, for example:

An overview of efficacy and safety of ambroxol for the treatment of acute and chronic respiratory diseases with a special regard to children

The exact dosage is not critical, so you may choose to dose their drinking water. About 2.5 mg ambroxol per 250 ml water works out about right, going by this table: Rat and Mouse food and water consumption by weight. The taste is not objectionable at that dosage.

If you mix a 30mg pill in 6ml of water, you’d therefore put 0.5ml of the liquid in a 250ml drinking bottle.

If you use the pre-mixed ambroxol syrup, 15mg/5ml, then you’d add about 0.8ml per 250ml of water.