<< I have a new washing machine that drains more rapidly then the pipe size
will tolerate initially. It leaks for a monent and then is ok. >>
You've just described a perfect case of improper drain venting. With proper
venting a 1 1/2" drain pipe usually works fine, given the proper height, etc.
<< The house is older and does not have the new larger drain pipe >>
Size may not matter <G>. See above.
<< Is there a way to solve this problem without redoing the plumbing? >>
Probably not. Have competent plumber check over the system and price mods or
repairs to the vent, whatever. It may be less costly than you think. Some folks
drain washers into laundry tubs to mitigate such problems. HTH