I am not sure if your goal is to make copper sulfate. or just to dissolve some copper.
If you want a solution or salt of copper sulfate, one way you can make it is to dissolve copper into the copper II chloride, with HCl and 3% H2O2 and air like we normally do, or use the excess copper II chloride you probably already have on hand, add sulfuric acid to it, heating and evaporating the solution will drive off water first, then the chloride will be driven off as gases, the copper chloride in solution will be replaced with the sulfuric acid forming copper sulfate, which can be evaporated to bright blue crystals, with re-dissolving and re-crystallizing the crystals you can end up with some very pure crystals of copper sulfate. (Note the copper sulfate crystals are much easier to redissolve in boiling hot water before they are cooled or dried hard).
Dilute nitric acid can also be used to dissolve the copper as copper nitrate, which can then be made into a copper sulfate as described above.
There are also several other methods to get copper sulfate.
Search the forum for killing two birds with one rock, it gives a way to make copper sulfate as a byproduct, while you strip the gold from gold plated copper pins in one process.
With any chemical experiments with acids and metals, you should spend some time doing your research, in the safety section you will find some good information on the topics, and in dealing with waste products of toxic metal solutions, these simple processes can be dangerous, or even become deadly if done without an understanding of the safety needed to protect yourself and others.