You can try InP quantum dots. There are several reports of the synthesis using different precursors.

In ACS publication list, you can search about ZnS, ZnO, Si, InP, depending on what you have in mind to explore.

CuInS/ZnS core/shells is also an option to consider, depending on your applicaiton. The attached paper describes the synthesis. You can acheive a much broader wavelength range for absorption and emission with this material than you can with CdSe or CdS. CuInS2 can be tuned to emit anywhere from ~450-1000 nm. The synthetic conditions are not that different from the ones required for CdSe synthesis, and like CdSe the synthesis of CuInS2 is straight forward and fairly simple.

The literature contains many articles on II-VI dots made without Cd. Generally speaking Cd can be replaced by Zn, which will blue shift your materials optical properties , or Pb, which will red shift their abs/ems spectra, with respect to the Cd analogue. Hg can also be used, however due to its high toxicity it is now generally avoided. If you already have a synthesis in mind simply replace the Cd salt with its Zn or Pb analogue. I would also recommend a 2 to the power of 2 statistical analysis varying the metal and stabiliser concentration while keeping the non metal contraction constant. This is the quickest way to produce luminescent dots from a new synthetic route.

InAs/GaAs, or InGaAs/GaAs quantum dots grown by Stranski-Krastanov method have been widely studied.

There are a number of quantum dot system, with two main distinctions: epitaxial and colloidal. So the answer to your questions depends on which you mean. In either case, there are many different material choices, most of which have been named. I think I'd add to the above the (colloidal) Pb-chalcogenides as well. It likely depends on what you want to study, what application you have in mind, wavelength range you'd like to be in )for absorption or emission) etc.

Thank you for all information and great to share this discussion.