Upper bound on Chaitin's constant for lambda calculus and SKI combinatory logic
You probably want to look at David et al's paper, Asymptotically Almost All λ-terms are Strongly Normalizing:

We present a quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results show that asymptotically, almost all terms are strongly normalizing and that any fixed closed term almost never appears in a random term.
Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators), the result is exactly opposite. We show that almost all terms are not strongly normalizing. This is due to the fact that any fixed combinator almost always appears in a random combinator.

You should be able to cook up a bound from looking at the details of their proof.