If you are sticking wood to wood then an aliphatic glue is the best bet. I would use Super Phatic from Deluxe Materials **LINK** as it is the nearest thing to a woodworking equivalent to superglue and has the benefit of water cleanup with a damp cloth.
You will need to simulate the caulking between the planks. Two options for this are to lay black cotton thread between the planks or simply run an indelible marker pen down the plank edges before gluing them into place. Try a test piece first, However, mahogany decking is a bit unusual as the normal practice would be to use teak which can be reproduced in model form using lime planking but obviously the choice is up to you.
Colin