Is it normal for my newborn to not have bowel movement for 2 days?

Yes: Newborn can have 8 bowel movements per day or they don't have ny for a week.

Varies with feed: Your newborn should have an initial tarry poo within the first 24hrs.This signals that all the plumbing is hooked up.After primary clean out the pattern depends a lot on the feed. Bf kids can make a smear every feed or one giant poo every week or so.Formula fed kids tend to go at least daily.If the kid is quiet & seems ok i wouldn't be concerned.If babies fussy, it may or may not be an issue.

Can Be: Some children have 10 bms per day and some may go once a week. As long as the baby is happy, thriving and in no apparent pain, both these extremes are normal for that child. If you still are concerned, call your pediatrician.