The original tips from OK Industries for the SAI-690 are the S9 series, including S9-108S, S9-116S, S9-203S, S9-208S, S9-305S, S9-306S, S9-312S, S9-320S, S9-112L, S9-201L, S9-202L, S9-204L, S9-308L, and S9-319L. The hundreds digit indicates tip shape, 1=bevel, 2=conical, 3=chisel; and S suffix are Short tips, L are Long tips for extended reach. The last two digits are approximately the tip width in hundredths of inches.
This differs from the tips for the SAI-640, which are the S4 series. The same nomenclature is used, but the catalog includes S4-105S, S4-106S, S4-202S, S4-304S, S4-305S, S4-306S, S4-308S, S4-309S, S4-201L, S4-203L, S4-208L, S4-304L, S4-305L, and S4-312L.
As you can imagine, the OK Industries stations were obsoleted in the 1990s, and they don't make these tips anymore since the merger with Metcal. The shape of the tips is similar to several Hakko models, but without dimensional data from micrometer measurements it would be hard to recommend a specific series. The SAI-640 is supposedly compatible with the Hakko 900M series of tips, which was renamed the T18 series. Since the SAI-690 is a larger version, it would make sense if it was compatible with a corresponding larger Hakko series, whether the 900L series, or DASH or MACH-I or 455, I couldn't say.
There were third-party manufacturers of compatible tips, of which Plato and Vanier were probably the biggest ones. Plato is still in business (acquired by TechSpray), and Vanier I'm not sure about. Plato doesn't list the S4 or S9 in their cross-reference, but Vanier did and those tips ("VAxx") may still be available somewhere. A.P.E. also makes compatible tips for some machines but I think they stopped making profiles other than the Pace ones.