This year, parents are eligible to claim a new credit on their taxes for all of their childrenâs arts-related activities in 2011. Similar to the fitness credit, you can claim up to $500 per child, which can result in a maximum $75 savings.hild Tax Credit. Every year, families can claim a certain amount for each child under 18. This year, that number is $2,131, which works out to a savings of around $320 per child. Either parent can claim it.