The City Council held hearings Tuesday on four new bills aimed at restricting guns in the Bronx and city. The bills include a gun offender registry, stricter purchase limits, and a ban on coloring kits that make guns look like toys. Officials say the bills will complement a new state law mandating a three and a half year minimum sentence for possession of a loaded handgun. However, with a right to bear arms enshrined in the Bill of Rights, council members say gun lobbyists are sure to sue the city on the constitutionality of such restrictive gun laws. The bills come as homicide rates in the Bronx are on the rise. There have been 63 murders so far this year, compared with 55 the same time last year. The bills, which have the full support of the City Council and the mayor, are expected to pass in the next few months.