What you would use here, but or and? "beating them" is a new idea or exception of the first idea?
There are several effective ways to discipline a preschooler, but\and beating them is completely inhuman.
Also more examples will be very helpful.
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'But' is a conjunction that is used to introduce a statement or clause that will be in contrast or different from what has already been mentioned.
'And' is a conjunction that is used to connect statements or clauses that are similar.
In your example, the conjunction 'but' would be better. The speaker is contrasting disciplining a preschooler with being completely inhuman. As a native American speaker this sentence sounds natural and better conveys the intended idea:
There are several effective ways to discipline a preschooler, but beating them is completely inhuman.
You could also use the word 'however' in place of 'but'.