While the gates of Gaya-ji are always open for Pitra Karma any day of the year, certain times are especially auspicious for performing Shraddh in Gaya:
Pitru Paksha Mela: This 15-day period (usually September-October) is the absolute peak time. Lakhs of pilgrims come to Gaya during this fortnight dedicated solely to ancestors. Performing Shraddh in Gaya during Pitru Paksha is considered immensely powerful.
Throughout the Year: Any day is suitable. Many perform Shraddh in Gaya upon visiting, regardless of the date.
Amavasya (New Moon): Monthly new moon days are auspicious for Pitra rites.
Solar/Lunar Eclipses: These are also considered potent times for such rituals in Gaya.
Basically, whenever you come to Gaya with sincere devotion, the time is right.