After conversion, Paramount OS is super squirrely All,

I have a custom made Paramount OS from 1991. I converted the bike to be my bike for family rides. To do this, I replaced the handlebars and put larger tires on the rim ~ nothing crazy, just a broader, more durable road tire.

The bike is beyond squirrely. Prior to the conversion, it was easy to ride no handed (Paramount's didn't have the shortest wheelbase's or the most aggressive geometry), now it's actually difficult to ride with one hand on the bars, let alone none.

EDIT-

BY squirly, I mean the bike's handling is loosey-goosey,touchy,unstable etc. I swapped from Cinelli drops to a straigh-bar, don't know the length. No trouble with the fork, headset and no other changes. Perhaps the weight dist. is off as someone suggested.
I turned this bike into a kicker as I wanted to upgrade to shifters on the drops, but the rear triangles on my OS were too narrow to accommodate the 8 gear cassette.
FH

What might be causing this?
If the headset is good then you need look at tire balance  

The tire itself could be out of balance and also it could not be seated evenly.  

Examine how tires are seated.

Put it on a stand or upside down and see if the wheels hold in position. Rotate 1/8 turn and check all 8 positions.  

For the rear you can spin the pedals - at high speed does it wobble?

If not balance then pull the tire and remount it.