Several dry winters and a series of fires are believed to have sent coyotes in record numbers onto Solano County ranchlands in search of prey, according to landowners. Richard Emigh, owner of one of the largest sheep ranches in the area, said coyotes have killed about 60 of his lambs, worth a total of $10,000. County agricultural officials said the animals caused an estimated $44,000 in damage to livestock and equipment in 1986-87, the last period for which figures were available. That figure is $7,000 more than the previous comparable period. It also is expected to grow for the next year.