A Shudra must perform Shraddha on a daily basis. (A Shraddha or rite to deceased ancestors can be performed daily, monthly or even yearly).
Because, the performance of Shraddha makes use of the Mantra "Swadha", which every one, including the Shudra, can utter, as says the following verse:
Manu Smriti 2.172. (He who has not been initiated) should not
pronounce (any) Vedic text excepting (those required for) the
performance of funeral rites, since he is on a level with a Sudra
before his birth from the Veda.
And, according Yajnavalkya Smriti's Chapter 1 verses given below, a Shudra should perform the Pancha Maha Yajnas ( Deva, Pitru, Rishi, Manushya and Bhuta Yajnas) as well, using the Mantra "Namas" or Namaha.
The service of the twice born, is the duty of a Sudrah, if he can not
maintain himself by that, he may become a tradesman, or he may
maintain himself with various works of art, but he should always do
good unto the twice born (120)
[He should be] devotedly attached to his wife, be protector of
servants and given to the performance of Shraddha. With the recitation
of the Mantram- Namas, he should perform the five Yajnas. (121)
Abstention from cruelty, truthfulness, not stealing, purity, control
of the senses, charity, mercy, self-restraint and forgiveness, are the
religious practices for all. (122)
Apart from the ones mentioned above, a Shudra is not required to perform any other rituals on a daily basis.