You can export a report, but this only saves these reports. You can however export specific tables and you obviously need Connector Solution to do this, but if you need specific associations which cannot be picked up by these rules, you will not be able to.
This solution should be easier and in the end, the reports are just a view of specific fields of specific tables. Try it this way:
1. Config Tab> Server Settings > Notification Server Infrastructure > Data replication. Here you find 2 folders; Data Sources and Import/Export Rules.
2. Right click on Data Sources, choose New, then CSV File Data Source. Choose a name for your data source on de-select Allow Imports. Select Allow Exports. When performing an export: choose Write data to a new file for every export.
3. Browse to the location where you want this file and click OK.
4. New File name prefix: I use my own prefix to identify the start of each file, which is then easier to identify the exports. It will add the date after the prefix you choose.
5. Maximum file size (Kb) I normally change to 2000, but you can experiment when you run your first one and change this.
6. Save your data and test data source.
7. Now right-click on Import/Export Rules and choose New > Resource Import/Export Rule. Name your rule.
8. Data Source: select the data source you just created.
9. Choose your Resource Type eg Computer and choose Export at Replication Direction:
10. You should see all the fields which would be available to export and you will also find all associations from that resource to other tables.
11. Save and execute the rule. check the data in the folder you selected under Data Sources. If this is what you want - remember to Enable the Schedule: on the Export Rule.