Whether two words rhyme is not a matter of objective fact that can be mechanically measured, it's a matter of classification and judgment by speakers of the language (let's stick to English). What you can do is test whether a particular rule satisfactorily matches the feelings of speakers. The majority of speakers operate with a single category "rhyme" but there are dozens of rhyme subtypes (perfect rhyme, half-rhyme, assonance, consonance). Zwicky's rhyme paper pulls together and describes the characteristics of leading subcategories in one genre.
The main problem is that this is a metalinguistic task that requires your subjects to agree on what the essential term is ("rhyme"). People do not agree on what counts as a "rhyme", just as they don't agree on the number of syllables in certain words, or where the syllable boundaries are. There are general trends: the problem is that you have to survey a reasonably large random sample of English speakers, in order to really get at what people think a "rhyme" is.
Probably, the most-accepted definition of "rhyme" is based on the final "foot" which is all of the syllables from the main stress to the end. The rule would require the feet be the same, except the onset consonants of the syllable on the left are different. Thus "crazy, hazy, lazy" rhyme; "forest, florist" do; "carry, scary" do, likewise "luminary" and "seminary".
You can use an online resource like this, which lists the words it calculates to be rhymes. I disagree with their results. Perhaps the best method would be to survey a panel of poets, if you can distinguish poets from non-poets. It's possible that I'm a poet and just don't know it.
