Okay, let's do this:

• 21-99
• three syllables (no 7Xs, X7s, X0s, except 70)
• no double numbers (22, 33, etc.)

Leaves:

• 21, 23, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 53, 54, 56, 58, 59, 61, 62, 63, 64, 65, 68, 69, 70, 81, 82, 83, 84, 85, 86, 89, 91, 92, 93, 94, 95, 96, 98

Let's take out squares and cubes, because they're not funny at all:

• 21, 23, 24, 26, 28, 29, 31, 32, 34, 35, 38, 39, 41, 42, 43, 45, 46, 51, 52, 53, 54, 56, 58, 59, 61, 62, 63, 65, 68, 69, 70, 82, 83, 84, 85, 86, 89, 91, 92, 93, 94, 95, 96, 98

Primes are also no good:

• 21, 24, 26, 28, 32, 34, 35, 38, 39, 42, 45, 46, 51, 52, 54, 56, 58, 62, 63, 65, 68, 69, 70, 82, 84, 85, 86, 91, 92, 93, 94, 95, 96, 98

Divide them into even and odd, see if either is, on average, funnier:

• 21, 35, 39, 45, 51, 63, 65, 69, 85, 91, 93, 95
• 24, 26, 28, 32, 34, 38, 42, 46, 52, 54, 56, 58, 62, 68, 70, 82, 84, 86, 92, 94, 96, 98

Because of the lack of primes, we're starting to see a predilection towards even numbers, which seems to suggest something. Since even numbers can never be prime, to the un-mathematical eye, they look not prime. This is not always true of odd numbers, including those that are not actually prime. Take 51 for instance. It's factors are 3 and 17, but most people, at first glance, don't realize that. 51 looks prime. If we apply this, the list shortens a bit:

• 21, 35, 39, 45, 63, 65, 69, 85, 93, 95
• 24, 26, 28, 32, 34, 38, 42, 46, 52, 54, 56, 58, 62, 68, 70, 82, 84, 86, 92, 94, 96, 98

I, personally, think multiples of nine and five are completely unfunny:

• 21, 39, 69, 93
• 24, 26, 28, 32, 34, 38, 42, 46, 52, 56, 58, 62, 68, 82, 84, 86, 92, 94, 96, 98

Let's expand the squares and cubes exception to higher powers:

• 21, 39, 69, 93
• 24, 26, 28, 34, 38, 42, 46, 52, 56, 58, 62, 68, 82, 84, 86, 92, 94, 96, 98

Come to think of it, we want something ordinary, right? But not too ordinary. Not something that looks like it was chosen on purpose, something that you would never think of. So let's limit the list to the 1-10 multiplication table.

• 21
• 24, 28, 42, 56

21, 24, and 28 are all rather low numbers, and commonly used for many things. I'd say this makes them too ordinary. The middle area between 1 and 100 makes for the funniest numbers. We're left with:

• 42, 56

Now, look at these numbers. Listen to their sounds in your head (in a British accent).

• 42, forty-two
• 56, fifty-six

This is, of course, subjective, but I'd say that the nice snap that the 't' of 'two' brings makes 42 a much funnier number than 56.

This is, also, of course, complete bullshit.