I have tried many times to to repair a cracked bird bath and its never worked for long.
I have got two suggestions. use something like this which is glass
http://www.amazon.co.uk/White-Glazed-Garden-Saucer-Plant-er/dp/B0095F8VSY My local garden centre also sells very large glazed earthenware pot saucers, the one I have is about 12 in in diameter.
or
Weigh the plastic one down with a heavy garden ornament.
or weigh the tray down with a piece of rock that grows moss. I have got a rather good piece of waterworn sandstone covered in moss on mine. the bird perch on it and it absorbs water from the birdbath which keeps the moss green.