Can two parents with negative blood types have a child with a positive blood type?
Short answer, no. If you are talking about either the ABO system, or Rh factor, one of the parents must have one of the antigens in order to produce a child with it. To back up a bit: there are 3 possibilities for antigens on red blood cells in humans--A, B, or no antigen (O). Humans have a combination of the 3, with "O" really meaning a lack of an antigen, or negative for an antigen. The possibilities for combinations are AA, AO, BO, BB, AB,or OO (negative). People with the first twocombos listed show blood type A; the next 2, type B; then AB, then O. If both parents are "negative", then they are both OO and have no gene for an antigen to pass on; they both contribute an "O", and the child is also OO.
Rh factor is simpler. You either have Rh factor, or not. If neither parent has the factor (Rh negative), they only produce offspring that have Rh negative blood. If either one is +, the child can be +. This is where a problem arises--an Rh negative mother carrying an Rh+ baby usually has no problem with that child, but the baby starts the mother producing antibodies against the Rh antigen. Later pregnancies can then have severe problems due to the mother's immune system attacking the fetus.