Can anyone help please?

My garden Shed roof is leaking due to sagging. The roof is 11 foot 6 x 7 foot 6 with a 6 inch drop.
The shed was handbuilt (poorly) by the previous owners and is covered in felt over tongue and groove boarding. The 2 supporting beams are along the long axis rather than the shorter one. Each "beam" is are made out if 2 lengths of 1 1/2" x 1 1/2" with a short length of the same bracing them at the join (something like -_- ). This has caused the centre of the roof to sag and leak. I have tried bracing the roof with poles and sealing the joins of the felt with bitumen paint with limited success.
Can anyone suggest a good to fix this? I am reluctant to replace the entire roof as I'm not that adventurous with DIY and I don't the weather will be kind enough to allow me an extended fixing period.