Can a doctor diagnosis pneumonia in a child 3 and a half years old without a radiography?

Yes. Pneumonia is often diagnosed clinically based on history and physical exam. Pneumonia may change the breath sounds heard with a stethescope by the physician. Chest xray is done at times to help determine the extent of the pneumonia or if the child is not responding to treatment.
Sometimes. To find it on x-ray, it must have been there long enough to acquire extra density of reactive fluid in the tissues of the lung. Breath sounds and pattern of illness can often allow a firm diagnosis hours if not a day or so before the x-ray turns positive.In the same way, the patient can be well into resolution with treatment days or weeks before the x-ray returns to normal.
Yes. Most times pneumonia is diagnosed without an xray. Classic symptoms that accompany a pneumonia in a child are fever, cough, fast breathing rate, occasionally shortness of breath and crackly sounds on examination with a stethoscope.