Lovebirds are not strongly sexual dimorphic, so it is difficult to distinguish male from female birds. However, differences in the size and shape of the head, the size of the overall bird and the width of the pelvis can act as guides as to the sex of a particular lovebird. Behavior is also suggestive of the sex of the bird.
Female lovebirds are often slightly larger and more robust than males. Their heads are smaller relative to the rest of the body. Female lovebirds have wider pelvises to allow for the smooth passage of eggs, so they will sit with their feet further apart than males. Experienced breeders will palpitate the pelvic bones by firmly gripping the bird and feeling under the tail. A male's pelvis will feel pointier, stiffer and more narrow.
The way birds pair up is not a good guide to sexing, as lovebirds do not pair in strictly heterosexual bonds.
Other, more reliable behavioral cues include dominance and nest building. In lovebirds, it is the female that builds the nest, and they will tuck and carry nesting material for just such a purpose. Females are also dominant over males. So, if a bird in a pair is encountered who is larger, more dominant, and is building a nest, it would be reasonable to deduce that bird is the female.