Generate RSA-2048 private key for a VERY fast decryption (don't care if it will be unsecure) Given public standard RSA exponent e = 65537,
is there any (d, n) pairs so that RSA decryption becomes a trivial operation?  

The modulus n must be no less than 2048-bit. The goal is to get a real certificate for some internal server that must send same data both via http and https. Certificate authorities will check modulus length. But some of them can possibly accept other e values so it can be a viable option too.

Note: security is not a factor at all, only simplicity\speed matters (trivial complexity will be an ideal).
Actually, if you're willing to consider a somewhat larger $e$, I found a solution that makes the decryption part real cheap.

This solution has $e = 446185741$ and $n =  3*5*7*11*13*23*29*31*43*47*53*61*67*71*79*103*131*139*157*191*211*229*239*277*331*419*421*443*461*463*547*571*599*647*661*691*859*911*967*1013*1021*1093*1123*1327*1381*1429*1483*1597*1871*1933*2003*2311*2347*2381*2531*2731*2861*2927*3037*3221*3571*3877*3911*4421*4523*4621*4831*5237*5981*6007*6271*6917*7411*7591*8581*8741*8779*8971*9283*9661*10627*10949*11731*12541*13567*14821*17291*19381*20021*20333*20749*21319*25117*28843*29173*29717*30941*35531*36709*38039*43891*46411*51613*51871*58787*62791*72931*78541*91771*92821*102103*106261*106591*111827*113621*134597*135661*138139*145861*163021*197341*213181*251941*258061*276277*304981*336491*355811*426973*445741*461891*520031*554269*602141*624037*749893*782783*903211*1118261*1193011*1381381*1492261*1749749*1806421*1939939*2134861*2348347*2624623*2704157*2771341*2897311*3233231*3354781*3749461*8112469*13123111*17160991*40562341$

Unless I miscalculated something (a real possibility), the corresponding decryption exponent is $d=1$; I believe that satisfies your requirement as to a "trivial" operation.