It costs a lot after a child is born, so I am very thankful.
It is expensive after a child is born, so I am very grateful.
It costs a lot of money have a child after it is born so I am very thankful.
「子供が生まれた後はお金がかかるのでありがたい」は英語ではこのようです。
(1) It costs a lot after a child is born, so I am very thankful.
(2) It is expensive after a child is born, so I am very grateful.
(3) It costs a lot of money have a child after it is born so I am very thankful.
「ありがたい」は英語では thankful や grateful になります。
「子供が生まれた後」→ after a child is born
「お金がかかる」→ to cost a lot (of money); to be expensive
ご参考までに。
アメリカ合衆国 
