You could do it by working off the same ideas as affine gap alignment (see these random lecture notes or these ones).

The affine gap algorithm uses three dynamic programming matrices to optimize the alignment: (1) the best score of two prefixes that ends in an aligned character, (2) the best score of two prefixes where the first sequence is in a gap, and (3) the best score of two prefixes where the second sequence is in a gap. The transitions and scores are set up so that you pay an extra penalty when you open a gap (move from matrix 1 to 2 or 3), but not when you lengthen an existing gap (stay in matrix 2 or matrix 3).

So based on those ideas, you would need a matrix for each possible distance since the last gap in each sequence (0, 1, 2, 3, 4, or 5+), for each of the two sequences. You could set up the transitions so that each additional aligned character goes "up" a matrix (for example matrix 3 to matrix 4, then matrix 4 to matrix 5+, and finally staying in matrix 5+). You would pay an extra penalty for adding a gap near a previous one (going from matrix 1-4 to 0), but not after you're sufficiently far away (matrix 5+ to 0).

There are a lot of details, and in general it might be annoying to implement. And, as some of the other answers suggest, it's not clear if it's a valid assumption or what it might correspond to biologically. But it can be done, and in the same time complexity as standard Smith-Waterman alignment as long as the maximum tracked inter-gap distance is regarded as a constant.

The answer to the OP is to increase the gap-open penalty, relative to the gap-extend penalty, to penalize multiple gaps over a region that seems to "need" gaps; this tunable ratio is what guides Smith-Waterman (and related algorithms) to consider more frequent, short indels vs. less frequent, longer indels.

Sounds harmless as a modification at first glance, however it is a very big modification (in addition to that it is not feasible with standard SW). In fact, it is a statement about a different model of sequence evolution. What you are saying is that neighboring indels occur less frequently or are more deleterious. You'd better have a very good reason to deviate from the standard (null) model for any serious analysis, otherwise you will just confirm your prejudice. Do you have such evidence, that this is the case wherever you look in the genome? Note that a modified aligner would not necessarily replace an indel with a longer gap opening, but might find very different alignments. Also, you could not use it to reject the null hypothesis, because it is already biased.

The standard algorithm doesn't track the exact length of an indel, but if this is vital to whatever you're doing you could certainly modify it to do so. There's no amount of penalty score tweaking that will do this without changing the algorithm itself.