Can I act as SIC with these specific type ratings?
The single B-737 type rating includes all variants of it, from the -100 through the Max; if you were typed in a -200, you have the type, so there is nothing else required in that regard to be Second In Command (SIC) on a 737 NG. (Source... my experience, having flown the -200, classics, NG's, and the Max, all with the one &quot;B-737&quot; type on my certificate.)
The DC-9 family is similar; I don't think there is a separate type for the MD-80.
That all said, there are other requirements pertaining to recency of experience and training. The other answer by @wbeard52 covered these. The pilot would also need a current medical. But as far as required ratings, those mentioned in the original question are sufficient.