Two axis plotting functions copied from http://forums.wolfram.com/student-support/topics/18949

TwoAxisPlot[{f_,g_},{x_,min_,max_},frange_,grange_,(opts___)?OptionQ]:=Module[{old,new,scale,pts,gstuff,fstuff},{fm,fM}=frange;
{gm,gM}=grange;
scale[var_]=((var-gm)*(fM-fm))/(gM-gm)+fm;
old=AbsoluteOptions[Plot[g,{x,min,max},Frame->True,PlotRange->grange,DisplayFunction->Identity],FrameTicks][[1,2,2]];
new=(Prepend[Rest[#1],scale[First[#1]]]&)/@old;
Plot[{f,scale[g]},{x,min,max},Frame->True,PlotRange->frange+{0,.05 (fM-fm)},FrameTicks->{Automatic,Automatic,None,new},PlotStyle->{{RGBColor[1,0,0]},{RGBColor[0,0,1]}},FrameStyle->{{},{RGBColor[1,0,0]},{},{RGBColor[0,0,1]}},opts]]
TwoAxisPlot[{x^3,Sqrt[x]},{x,0,4},{0,64},{0,2}]
TwoAxisPlot[{Sqrt[x],x^3},{x,0,4},{0,2},{0,70}]

TwoAxisListPlot[f_List,g_List,frange_,grange_,color1_,color2_,opts___?OptionQ]:=Module[{old,new,scale,fm,fM,gm,gM,newg},{fm,fM}=frange;
{gm,gM}=grange;
scale[var_]:=((var-gm) (fM-fm))/(gM-gm)+fm;
old=AbsoluteOptions[ListPlot[g,Frame->True,PlotRange->grange,DisplayFunction->Identity],FrameTicks][[1,2,2]];
new=(Prepend[Rest[#1],scale[First[#1]]]&)/@old;
newg=Transpose[{Transpose[g][[1]],Map[scale,Transpose[g][[2]],{1,2}]}];
ListLinePlot[{f,newg},Frame->True,FrameTicks->{Automatic,Automatic,None,new},PlotStyle->{{color1},{color2}},FrameStyle->{{},{color1},{},{color2}},PlotRange->frange*(1+.00 (fM-fm)),opts]]

data1={{1,6.607369758576875`},{2,6.455696202531636`},{3,6.666666666666665`},{4,6.724782067247825`},{5,6.956521739130417`},{6,7.187112763320935`},{7,6.985294117647078`},{8,7.212713936430326`},{9,7.551766138855065`},{10,7.515151515151519`},{11,7.367149758454117`},{12,7.340553549939832`},{13,7.389749702026216`},{14,7.253269916765759`},{15,7.193396226415105`},{16,7.001166861143515`},{17,6.9686411149825656`},{18,7.052023121387263`},{19,6.987399770904945`},{20,6.727480045610035`},{21,6.56851642129106`},{22,6.5388951521984096`},{23,6.749156355455566`},{24,6.8385650224215055`},{25,6.9922308546060075`},{26,7.206208425720617`},{27,7.370737073707345`},{28,7.742639040348953`},{29,7.926167209554857`},{30,7.883369330453571`},{31,7.922912205567445`},{32,8.119658119658135`},{33,8.076514346439968`},{34,8.042328042328029`},{35,7.692307692307687`},{36,7.660020986358873`},{37,7.676348547717837`},{38,7.652533609100298`},{39,7.479508196721318`},{40,6.68016194331984`},{41,6.539235412474853`},{42,6.406406406406395`},{43,6.448412698412698`}};

data2=Map[{0,456}+#&,{{27,1.675041876046901`},{28,1.4827018121910784`},{29,1.379870129870131`},{30,1.9215372297838096`},{31,2.0816967792615992`},{32,1.8468641785302164`},{33,1.3222516055912514`},{34,1.715137956748669`},{35,1.9428152492668493`},{36,1.4742898238043756`},{37,1.5591778880226892`},{38,2.267969295184913`},{39,2.3882633913340445`},{40,1.6327890703098813`},{41,1.1803278688524488`},{42,1.8794556059624101`},{43,1.6221374045801484`}}];

Labeled[Labeled[TwoAxisListPlot[data1,data2,{5,8.3},{450,460},Red,Blue,Axes->False,Joined->{True,False},PlotMarkers->{Style[○,Red,Medium,Background->White],Style[▲,Blue,Medium]}],{Style["X",FontFamily->Times],Style["Y",Red,FontFamily->Times]},{Bottom,Left}],Style["Y-alt",Blue,FontFamily->Times],Right]

Now attempt to modify TwoAxisListPlot to TwoAxisDateListPlot