There are a few things you can do:
1) Explore the structure of the English syllable and generate syllables, following these rules.
2) Use Markov chains to obtain a statistical model of English phonology.
There are many resources on Markov chains, but the main idea is to write down the probability that a particular letter will be after a certain sequence. For example, after "q", "u" is very likely; after "k", "q" is very unlikely (this uses Markov chains of length 1); or, after "th", "e" is very likely (this uses 2-length Markov chains).
If you are following a syllable model route, you can use resources such as this to help you figure out your intuitions about your language.
UPDATE
3) You can make it much simpler without modeling full English, but, say, Japanese or Italian, where the rules are much simpler, and if it is a meaningless word, then it is easy to remember as a meaningless English word. For example, the Japanese have only about 94 valid syllables (47 short, 47 long), and you can easily list them and choose at random.
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