[RPG] Can a cleric prepare spells later in the day

Yes, he can.

As per PFSRD,

Until he prepares spells from his spellbook, the only spells a wizard has available to cast are the ones that he already had prepared from the previous day and has not yet used. During the study period, he chooses which spells to prepare. If a wizard already has spells prepared (from the previous day) that he has not cast, she can abandon some or all of them to make room for new spells.

There is no obligation to drop those extra prepared spells; moreover, you could change your selection of additional spells prepared (but not the selection of spell slots they are in).

As a side note, a scroll or wand of Mnemonic Enhancer (or, rather, the retain option of the spell) would not be terribly effective, since you must cast it on the round following the casting of the spell you wish to retain.

Yes.

From the Hypertext d20 SRD:

Divine spellcasters prepare their spells in largely the same manner as wizards do, but with a few differences. […]

Spell Selection and Preparation

A divine spellcaster selects and prepares spells ahead of time through prayer and meditation at a particular time of day. The time required to prepare spells is the same as it is for a wizard (1 hour), as is the requirement for a relatively peaceful environment. A divine spellcaster does not have to prepare all his spells at once. However, the character’s mind is considered fresh only during his or her first daily spell preparation, so a divine spellcaster cannot fill a slot that is empty because he or she has cast a spell or abandoned a previously prepared spell.

From d20PFSRD:

Spell Selection and Preparation

A divine spellcaster selects and prepares spells ahead of time through prayer and meditation at a particular time of day. The time required to prepare spells is the same as it is for a wizard (1 hour), as is the requirement for a relatively peaceful environment. When preparing spells for the day, a divine spellcaster can leave some of her spell slots open. Later during that day, she can repeat the preparation process as often as she likes. During these extra sessions of preparation, she can fill these unused spell slots. She cannot, however, abandon a previously prepared spell to replace it with another one or fill a slot that is empty because she has cast a spell in the meantime. Like the first session of the day, this preparation takes at least 15 minutes, and it takes longer if she prepares more than one-quarter of his spells.

(emphasis added to both quotes)

The "particular time of day" clause limits them only as far as the first daily spell preparation, i.e., the one in which they regain spell slots.