First things first you aren't going to be able to get longitude without an accurate clock and/or a tome of sight reduction tables. Without those aids which you'd be hard pressed to create while marooned on an island your navigational options are limited. The best you can really hope for is to follow a latitude line/plane.
I think a cross staff would be an effective celestial navigational aid that could be improvised and allow you to follow a latitude line.
Normally the shorter cross piece would slide up and down the length of the staff to allow you to measure angles. That is going to be too hard to calibrate, unless you know the angles between enough stars to calibrate it yourself. If you can calibrate the cross staff then you can pick the latitude you want, sail to that plane and turn east or west to follow it.
If you can't calibrate it you need to sit on your boat at night and adjust (whittle) the length of the shorter cross piece so it lines up with the North star or the Southern Cross and the horizon. Once this is accomplished then you can maintain your current latitude by repeating the sighting and correcting as needed.
Another option for latitude based navigation would be a Sun Compass.
Of course the Achilles heel of this device is the sun's height varies increasingly as you move away from the equator. The proper name for this pattern is an analemma.
Due to this variance you need to be lucky and be close to the equator and make corrections with your cross staff as needed. As such this should be considered a supplementary aid, not a primary aid.