Do we have a graph of how sedimentation rates changed over time?
Sedimentation rate presently varies many orders of magnitude depending on the place you observe. The rate of sedimentation is also different. Some places have continual sedimentation, others have episodic sedimentation events.
That is why charts that show changes in sedimentation rate are usually done for individual sedimentary basins, to determine the basin evolution. This is available for many basins, especially if they are of interest to the hydrocarbon industry.
As Spießbürger also mentions in his answer sedimentation rates are local, and highly depend on sediment supply and accommodation room in the sedimentary basin. Global sedimentation rates are then just an average of all sedimentary basins, and are closely related to global erosion rates, although not necessarily the same depending on the time scales you look at, as dissolution of minerals doesn't directly lead to sedimentation, and eroded material can be trapped in for example a glacier for a substantial amount of time. The erosion rates then depend on the amount of erodable material (so topography, vegetation cover, etc.) and climate conditions providing some means of transport.
All in all globally averaged sedimentation rates could be calculated, but are in the end such an indirect effect of wildly varying causes, while at the same time not providing much meaningful data, that it's probably not something worth investing much time in.
There is not enough data resolution at the moment, neither spatially nor temporally. There are geological periods thought to have undergone higher erosion rates based on the abundance of some sediment facies, such as during the Trias. There are also many sedimentary basins where where the evolution of sedimentation rates is well known. But this depends strongly on local geographic/tectonic conditions, such as the available accommodation space of the tectonic subsidence, so it gives no information on what is going on at global scale. To make it even more difficult, there are good indications that we are biased in the ways we measure both erosion and sedimentation, exaggerating recent transport rates relative to longer term.
To have the global perspective you want, geoscientists need a coherent, world-wide, statistically representative set of past erosion or sedimentation measures, and that for each geological period. But erosion and sedimentation take years to be determined for a particular basin/orogen setting and for a specific period; the gaps are enormous.
The only roughly quantified period at a global scale is the Miocene-Pliocene-Quaternary. And even there the discussion is very open. The following studies suggest that global erosion/sedimentation rates have increased during the last 4-6 million years.
The first is based on a compilation of delta sedimentation rates:
Zhang, P., Molnar, P.& Downs, W. R. Increased sedimentation rates and grain sizes 2–4 Myr ago due to the influence of climate change on erosion rates. Nature 410, 891–897 (2001).
The second uses thermochronology, mostly Apatite Fission Track analyses:
Herman F, Seward D, Valla PG, Carter A, Kohn B,Willett SD, Ehlers TA. 2014. Worldwide acceleration of mountain erosion under a cooling climate. Nature 504: 423–426. DOI: 10.1038/nature12877
Both interpret the acceleration of erosion as a result of the changes in Earth's climate during that period: initiation of the glacial interglacial cycle in the northern hemisphere.
Due to the gaps in the geological outcrop record, and to our limited capacity of dating sediments, my bet is that it will take decades at least to have a reliable graph like the one you aim at.
Hope this helps.