Depends on your downstream application. If it's solely just to identify a target receptor then you can use a chemical cross linking aides such as BS3 from Thermo/Pierce.
I'm aware of two methods to covalently link a ligand such that it irreversibly bind to its receptors: this is either by using non-natural aminoacids (an example is provided in the following PMID: 23913257) or by using photoreactive groups. I have been using this method a long time ago in the group of Immanuel Luescher in Lausanne who was very fond of this technique: PMID 9670927 . As to be able to measure downstream functions, I believe that it's going to depend a lot on the biological system of interest. Sometimes, irreversible ligand-receptor interaction turns out to massively activate the receptors but sometimes, ligand-receptor dissociation is key to biological function (this was the case in our study) and therefore, you can hardly measure any function in this situation if you force irreversible binding. In addition, photoreactivity can also alter the cell viablility such that only early but nor late functions can be studied.