AS A B737-200 LANDS AT PVD; RI; THE 2 NOSE GEAR TIRES FAIL AND BLOW OUT. PLT IS DISAPPOINTED THAT IT TAKES SO LONG TO DEPLANE THE PAX AND HAVE THE ACFT TOWED OFF OF THE RWY.

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PROVIDENCE ATIS NOTIFIED US OF LLWS AND GUSTY XWIND CONDITIONS. TWR RPTED LOSS OF 15 KTS ON FINAL FROM A PREVIOUS ACFT. I ELECTED TO LAND AT FLAPS 15 DEGS FOR IMPROVED XWIND HANDLING AND GAR CLB GRADIENT; EVEN THOUGH AIRPLANE WAS 99000 LBS WITH A 7100 FT RWY. TOUCHDOWN WAS A GREASER; WITH GENTLE NOSE LOWERING. I BRAKED EXPEDITIOUSLY WITH ABOUT 1.4 EPR'S REVERSE THRUST. THROUGH ABOUT 90 KTS; IT SOUNDED AS IF A NOSE TIRE FAILED (NO NOSE GEAR BRAKES ON THIS ACFT); SO I PLANNED TO CLR RWY 5 AT THE NEXT TXWY AND HAVE THE ACFT LOOKED OVER BEFORE TAXIING ON THE REMAINING NOSE TIRE. HOWEVER; WHILE COASTING AT SLOW SPD; THE ACFT WAS NO LONGER STEERABLE WITH NOSEWHEEL STEERING; SO I COASTED TO A STOP ON THE RWY. INSPECTION REVEALED BOTH NOSE TIRES FAILED; SO I MADE THE CORRECT DECISION TO NOT CLR THE RWY. PAX WERE UNEVENTFULLY BUSSED TO THE TERMINAL. THE ACFT HAD BOTH RIMS/TIRES REPLACED AND CONTINUED FLYING AFTER ABOUT A 2 HR DELAY. I LATER REMEMBERED THAT ON TKOF FROM MCO; ACFT YAWED EVER SO SLIGHTLY TO THE L WITH CALM WIND CONDITIONS; JUST PRIOR TO ROTATION. I CORRECTED THE YAW; NOTED BOTH ENGS COOKING NORMALLY; AND ROTATED. PRIOR TO GEAR RETRACTION; A PACK TRIPPED; WHICH I IGNORED WHILE THE FO RESET IT. I SUSPECT A TIRE FAILED ON THE MCO TKOF; CAUSING DEBRIS TO ENTER THE RAM AIR INLET FOR THE PACK. THE REMAINING TIRE COULDN'T HANDLE THE INCREASED TOUCHDOWN SPD FOR THE WT/WINDS IN PVD; AND ALSO FAILED. SUPPLEMENTAL INFO FROM ACN 375329: ON ROLLOUT AFTER A NORMAL LNDG WE NOTICED A SOUND WHICH INDICATED A FLAT NOSE TIRE. WE STOPPED ON THE RWY TO AVOID FURTHER DAMAGE. ATC CLOSED THE RWY (RWY 5 AT PVD) AND MAINT WAS CALLED TO CHANGE THE TIRE. THE PROB WAS THAT IT TOOK 1 HR TO GET BUSSES OUT TO UNLOAD THE PAX SO MAINT COULD WORK ON THE ACFT.