Getting the center and boundaries of cell of raster object in R

You can calculate those yourself, something like this should work, since you have the coordinate of the cell.

library(rts)
library(raster)
f <- system.file("external/rlogo.grd", package="raster")

r1 <- raster(f) 
nc = r1@ncols
nr = r1@nrows
d = r1@extent
point = c(15.5,20.3)
cellCol = colFromX(r1, 15.5)
cellRow = rowFromY(r1, 20.3)

xlen = d@xmax-d@xmin
ylen = d@ymax-d@ymin
cellXSize = xlen/d@xmax
cellYSize = ylen/d@ymax
XMinCoord = (cellCol-1)*cellXSize
YMinCoord = (ylen-(cellRow-1))*cellYSize
XMaxCoord = (cellCol)*cellXSize
YMaxCoord = (ylen-(cellRow))*cellYSize
bounds = c(XMinCoord,XMaxCoord,YMinCoord,YMaxCoord)
centerX = XMinCoord+(cellXSize*0.5)
centerY = YMinCoord-(cellYSize*0.5)
center = c(centerX,centerY)

plot(r1)
points(x=15.5,y=20.3,col="white", bg = "white", pch=16 )
points(x=centerX,y=centerY,col="black", bg = "black", pch=16 )
points(x=XMinCoord,y=YMinCoord,col="black",  pch=22 )
points(x=XMinCoord,y=YMaxCoord,col="black",  pch=22 )
points(x=XMaxCoord,y=YMaxCoord,col="black",  pch=22 )
points(x=XMaxCoord,y=YMinCoord,col="black",  pch=22 )

Let's test your statement that your method doesn't work. First make a simple tiny raster:

raster.data <- raster(matrix(1:12,3,4))

class      : RasterLayer 
dimensions : 3, 4, 12  (nrow, ncol, ncell)
resolution : 0.25, 0.3333333  (x, y)
extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : layer 
values     : 1, 12  (min, max)


given.point <- c(0.2345, 0.4567)
cell.target <- cellFromXY( raster.data , given.point )
benchmark.point <- xyFromCell( raster.data , cell.target )

and I see that the benchmark point is not the same as the given point:

> given.point
[1] 0.2345 0.4567
> benchmark.point
         x   y
[1,] 0.125 0.5

and if I plot them I can see it is doing it correctly:

So there seems to be nothing wrong with your method. You've not shown us the output values for your test point so we can't tell if you really don't get a difference or if you aren't seeing it because you aren't seeing enough decimal points or if your test point is actually on a cell centre.