I've been curious about this one for a while. We know they can - as evidenced by Persephone and the Rama-Kandra family - but how does it happen in the first place? Love comes about due to chemical reactions that occur in our brains. Machines, however, are physically different than humans.
How are they able to experience sexual impulses and love?
The script indicates that Neo is having problems coping with this one as well. The very short answer is that your prejudice (and his) prevent you from seeing that independent beings of free will and intelligence are perfectly capable of falling in love, procreating and striving to protect their offspring, all without the mucky messy business of squishy brains and thrusty groins.
It's clear that although their Rama and Sita's "love" is of a qualitatively different basis, Rama refers to it as thusly when inhabiting a human-shell and talking to a human.
Neo struggles with the idea of a Machine loving another Machine.
RAMA: You do not understand?
NEO: I just have never...
RAMA: Heard a program speak of love?
NEO: It is a human emotion.
RAMA: No, it is a word. What matters is the connection the word implies.
He reads Neo's code.
RAMA: I see that you are in love.
Neo feels awkwardly exposed.
RAMA: Can you tell me what you would give to hold on to that connection?
Matrix Revolutions - Original Screenplay
Interestingly, it's when machines go rogue that they begin to exhibit emotion such as love and hatred, implying that these "human-like" emotions are very much frowned upon by the machine mainframe.
AGENT SMITH: I don't know. If I knew...
Agent Smith hides his knotting fist. He is becoming angry. It is something that isn't supposed to happen to agents.
AGENT SMITH: Leave me with him.
The Matrix
Love comes about due to chemical reactions...
In biological life, logical reasoning, associative memory, and all knowledge and thought are also due to chemical reactions. The Machines, having simulated biological life to a high degree of accuracy (and themselves already being examples of Strong AI) should not have a problem in simulating the processes behind love.
In "The Animatrix", machines could be seen experimenting on humans, inducing and suppressing specific emotions. This likely would have increased their ability to understand and reproduce those processes. Reproducing the chemical reactions behind basic emotions should be even simpler than developing a complex intelligence. "Lesser" animals show emotional responses and bonding behavior that we often associate with love. Even the less-advanced Sentinels showed emotional capabilities. Human intellect, the ability to logically reason, and consciousness should be more difficult to create - yet the programs (like The Architect or The Oracle) are often depicted as being even more intelligent and aware than humans.
Beyond the "how" question is whether the independent thought and love the exile programs show is just a part of the simulation. We have no way of knowing if what they experience is the same as a human. Rama Kandra is obviously feeling something, but he just uses "love" as a placeholder to explain those feelings in human-terms.
It's also implied that there is something about human love that The Machines don't fully understand. The Architect knew enough to predict that Neo might choose love over Zion, but not enough to predict his actions after that - that he would sacrifice himself. That missing knowledge may be a factor in the systemic anomaly that leads to The One in the first place, which The Architect had previously been unable to eliminate despite all efforts.
