  The statistics of critical spin-spin correlation functions in Ising systems
with non-frustrated disorder are investigated on a strip geometry, via
numerical transfer-matrix techniques. Conformal invariance concepts are used,
in order to test for logarithmic corrections to pure power-law decay against
distance. Fits of our data to conformal-invariance expressions, specific to
logarithmic corrections to correlations on strips, give results with the
correct sign, for the moments of order $n=0-4$ of the correlation-function
distribution. We find an interval of disorder strength along which corrections
to pure-system behavior can be decomposed into the product of a known
$n$-dependent factor and an approximately $n$-independent one, in accordance
with predictions. A phenomenological fitting procedure is proposed, which takes
partial account of subdominant terms of correlation-function decay on strips.
In the low-disorder limit, it gives results in fairly good agreement with
theoretical predictions, provided that an additional assumption is made.
