Why does my baby's teeth popping out with some black discoloration at the tips?

Stain or decay?: This is most likely staining, although it could be decay. Make sure you have it looked at by a pedodontist (pediatric dentist) just to be sure. Also make sure your child does not go to sleep with a bottle with anything else in it other than water! otherwise your child can develop nursing bottle mouth syndrome which can be devastating to his\her teeth.

Blood clot: Possible blood clot. I would not worry about it.

Black discoloration: Do you mean "erupting" or "falling out?" How old is your child? Although discoloration may be due to any of a number of natural phenomena, the concern is always decay. All children should be seeing a General Dentist or specialist Pediatric Dentist from their 1st birthday onward. Please immediately take your child to his/her Dentist for examination. A cavity is an infection.