Stopping dirt in an unlined roof

[CPdiyer]

I see the problem of uncovered roofs elsewhere however, I am going to reinsulate the roof and throw down some boards just for storage.
My problem is with no lining the roof space gets real dirty real fast - any suggestions for something I can put on the inside for a short term fix.
A new roof is not an option at this time as the kitchen and boiler have drained the piggy bank

 

[noseall]

Tar-paper