The European Parliamentary Research Service (EPRS) does have some return proportions, but they are pretty dated and it's not totally clear to me if the figure is what you want; they measured "returns of illegally staying third-country nationals" so it may include more than asylum seekers:
The Civil Liberties, Justice and Home Affairs Committee of the European Parliament is considering
the 654 amendments, tabled in February 2019, to the European Commission's September 2018
proposal to recast the Return Directive. The Directive is the main piece of EU legislation governing
the procedures and criteria to be applied by Member States when returning irregularly staying third-country nationals, and a cornerstone of the EU return policy.
Taking into account the decrease in the EU return rate (45.8 % in 2016 and 36.6 % in 2017), and
following European Council and Council calls to review the 2008 legal text to enhance the
effectiveness of the EU return policy, the Commission has proposed a targeted recast of the directive
aiming to 'reduce the length of return procedures, secure a better link between asylum and return
procedures and ensure a more effective use of measures to prevent absconding'.
[...]
According to the Commission's explanatory memorandum accompanying the proposal, several Member
States have established maximum periods of detention substantially shorter than those permitted by the
Directive and that fact is preventing effective removals. However, in 2017, Spain (60 days maximum detention
period) had a return rate of 37.2 %, and France (45 days, although a change was introduced in 2018), of 15 %.
Among Member States with maximum periods of detention matching the maximum permitted by the
Directive (6 months plus 12 months), for example, the Czech Republic had a return rate of 11.2 %, Belgium of
18.2 %, Greece of 39.5 %, and Germany of 46.3 %. Although data on the average period of detention pending
removal is not available for every EU country and, therefore, clear conclusions cannot be drawn, the
comparison between the Member States' return rates does not seem to support the Commission's statement,
at least without any further explanation.
Also this bit is interesting
The Directive does not expressly deal with a common situation in return procedures. When a
returnee does not voluntarily leave the territory of the Member States, removal may become
impossible even if national authorities take all necessary measures to enforce a return decision, for
example due to the unwillingness of third countries or of the returnees themselves to cooperate in
the procedure. Articles 9 and 14 of the Directive provide for the possible postponement of removal
and impose some safeguards to be respected while return is pending. From a different perspective,
Article 6(4) allows Member States to grant authorisation to stay to any third-country national
irregularly staying on their territory for compassionate, humanitarian or other reasons. However, the
Directive neither obliges nor forbids Member States regularising those third-country nationals
whose return decisions cannot be enforced (C-146/14 PPU), leaving Member States a margin of
discretion to adopt such decisions, or opt for the indefinite postponement of removals, a decision
with severe consequences for the individuals concerned.
But there no stats how many returns failed because the target country failed to cooperate, even though it's said to be a common reason.
For Germany, Reuters reported in February:
Germany failed to deport 27,000 rejected asylum seekers last year, nearly half of the total 57,000 cases, Interior Minister Horst Seehofer said on Sunday, adding that the government would step up efforts to get those migrants out of the country.
Seehofer told Bild am Sonntag newspaper that the 27,000 rejected asylum seekers could not be deported because they had no travel documents or police could not find them. Some resisted deportation at the airport, he added.
The government plans to restrict the rights of failed asylum seekers who lied about their identify or who are deemed a security threat, by establishing a new form of “preparatory detention” before deportation, Seehofer said.
Those migrants would have to report regularly to police and they could face further restrictions such as having to wear a locator device, the minister said. The cabinet is expected to pass the law before the summer holidays.
There is a 2018 paper which covers the complexities of the national legislations on returns in EU countries; but it doesn't have any EU-wide or even country-level stats like you want.
The EU Agency for Fundamental Rights (FRA) does put out quarterly reports including some return figures but these are not very useful for computing the stats you want because they not related to the number of failed applications in the same time period; the return numbers are broken down by country, but for some countries, e.g. Hungary, there no figures even for that. And there are no summary tables, the report has a narrative form.
