38 weeks is the safest time for the baby to be born but intercourse will help labor come because the sperm will help your cervix thin just like when they do in the hospital with cervadil.
It wouldn't be wise to try and induce labor yourself at 37 weeks unless you had medical clearance because (although that is the accepted time for the premature birth cut-off point),some babies can still be immature at that age.This is particularly so with doubtful dates,and also because of the possibility of having become pregnant much later than it appears ( missed miscarriage and subsequent fertilization).