  For any finite unital commutative idempotent semigroup S, a unital
semilattice, we show how to compute the amenability constant of its semigroup
algebra l^1(S), which is always of the form 4n+1. We then show that these give
lower bounds to amenability constants of certain Banach algebras graded over
semilattices. We show that there is no commutative semilattice with amenability
constant between 5 and 9.
