The seasons of October and November are best, but everyone knows that and they come to Rajastan, so everything is costly too.
The off season, May to September is actually quite nice. Reason being the cheaper prices of accommodation and other activities. You ll have to avoid going out in the peak heat of the day, but the morning and evening shall be nice. You might experience some desert rain too. In the rainy season, cloudy skies make it pleasant even in the day. It is a risk though, with all the heat and rain. Proceed as per your physical conditions too.