Many parents buy into the concept of "benign" deprivation. This ultimately refers to saying "no" for every little thing that a child wants. The idea is to say "no" to most all of children's petitioned requests. However, not giving your child what they ask for all of the time can be seen as child abuse under God's Law.
God's Law on child abuse is spelled out in Colossians 3:21 KJV:
Fathers, provoke not your children to anger, lest they be discouraged.
The Greek root word translated "provoke...to anger" is ερεθιζο (Latin: erethizo) and refers to offenses or damages, namely the slightest of personal offense perceived by a child, including, but not limited to, the slightest of offensive touch or speech perceived by a child, stemming from entitlement, with this entitlement including any parent anger directed towards a child. The idea behind not abusing your child is to avoid offense in children. Avoiding offense in children involves, in part, not saying "no" to almost every little thing that they ask for. Children need to hear the word "no" only when absolutely necessary, meaning almost never. Parents should find every reason to tell their child "yes" as opposed to telling them "no". However, children will need to hear the word "no" at some point in their childhood, in which case a meaningful apology is in order for hurting a child's feelings, lest it officially become an offense. Usually, all that is necessary is a reassurance of good intent in the case of a child not accepting the word "no" when not given out of anger, such as "I'm sorry, but I had to set X limit for Y reasons". However, if you ever lose your cool with your child as a parent, including while saying "no" to a child, you definitely need to give a formal apology for hurting your child's feelings with your anger, such as "I apologize for losing my temper with you", and then commit to never losing your cool with your child ever again, as losing your cool in and of itself is entitlement, and was seen as entitlement in the Early Church. This commandment cross-references the Eighth and the Tenth Commandments, with the Apostle Paul here convicting a group of Greek Christian parents who brought into the church their pagan parenting customs, which were punitive in nature. Paul, contrary to popular legend, opposed any and all punitive parenting in his secular writings. Attachment parenting was banned under Roman law, but the Early Christians did it anyway, obeying God over men.
In the Early Church, parents found nicer-sounding ways of declining a request, such as "that won't work", "that can't happen", or "that isn't possible". Even in the case of clear fornication, which was something then that you confessed at your baptism, children were scolded in a reassuring manner, promising that "you will get a chance when you are older".
There is no need for a child to be deprived of items they want at the store. Maybe they already have the same toy at home, but don't question the petitioned requests of a child that far in. They are only asking for things from you because they associate the presents from the store with YOU.
Parenting in the Early Church was never motivated by anger. Instead, parenting was motivated by worry or concern, with disappointment being the only acceptable displeasure for children in parents. Parent anger directed towards a child was seen as akin to a viper lashing out at an unsuspecting child. Most arbitrary limits from parents come from anger, not worry or concern.
The depraved and entitled parents who provoke their children to anger through punitive parenting will not inherit the Kingdom of God! Let them be cast forever into the lake of fire and burning sulfur, which is the second death prepared for Satan and his accomplices! Let them descend into the abyss which is the ever-burning Hell of fire and torment, suffering God's Wrath day and night forever and ever! Repent, for the Kingdom of Heaven is at hand!