Half-day rates exist at some beach concessions — particularly if you arrive after 3–4 pm, when attendants would rather rent an unsold set cheaply than leave it empty. It is worth asking politely; a discount of 30–50% on the listed price for an afternoon slot is not unusual at smaller or less busy beaches.
Formal haggling on standard listed prices at the start of the day is uncommon and can come across poorly at organised bars. However, asking about a group rate if you are booking several sets or a baldahin for a whole party is perfectly normal and sometimes rewarded.
Quieter shoulder months — June and September — naturally bring more flexibility, as occupancy is lower and operators are more willing to negotiate. On Buljarica or the edges of Velika Plaza you may find informal rentals where a brief friendly exchange genuinely does influence the price.