Here's some pythonesque pseudo-code that might do it:

    for tweet in twitter_api.latest_tweets():
        phonetic_tweet = convert_tweet_to_phonemes(tweet)
        
        if is_iambic(phonetic_tweet):
            end_rhymes = extract_end_rhymes(phonetic_tweet)
            db.insert_iambic_tweet(tweet, end_rhymes)
            
            for end_rhyme in end_rhymes:
                rhyming_tweets = db.select_rhyming_tweets(end_rhyme)
                if rhyming_tweets:
                    rhyming_tweet = random.choice(rhyming_tweets)
                    return [tweet, rhyming_tweet]

There are several open source word lists out there that make this feasible.

I also wrote a filter over Twitter for iambic pentameter once, and had a friend write a web frontend to it. Here's my (messy) code; http://glozer.net/ wrote the frontend in Erlang but AFAIK never released it.

https://github.com/darius/versecop

Pentametron is cooler. I did try filtering for rhymes too, but there wasn't enough data in the free feed, at least back then.

I read somewhere that it uses the cmu pronouncing dictionary which would give it both the meter and rhyme it needs (http://www.speech.cs.cmu.edu/cgi-bin/cmudict)