You could always create custom single select lists for each of your projects and use those to indicate the project custom priority. You could even combine this with the current Jira priority field to have both a global priority and a project priority.
Atlassian is planning on making Project specific priorities available sometime: https://jira.atlassian.com/browse/JRA-3821
There's a couple different workarounds that you could try:
2. Create a separate priority select list custom field for each project. Then create a listener which will update Jira's Priority field with the value in your custom field.
As others have noted, changes to the Prioirites field is global across all projects.
The best workaround I have is to create a Custom Field. Make it a single-select field (like Priority) and name it "[project] Priority" - use the name of your project. Add the priority names you want and then set an appropriate default value (or it won't show up in existing tickets). You then have to add this Custom Field to a custom Screen Scheme and associate that custom Screen Scheme with your project.
You can move the custom field to where you want it by configuring the custom Screen Scheme (configure project --> Fields --> click on the Screen Scheme in question). You can drag and drop it to where you want it to go.
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