I am wondering if there are any verbs/phrases that qualify both as ditransitive, and as atelic. The following shows the relevant tests. The satisfying verb/phrase should have the same * patterns as give w.r.t. ditransitivity, but * patterns with sleep and watch in the telicity tests. A complete answer will provide the evidence that the proposed word passes the test in these ways.
(*'s in the below indicate low acceptability. Note that the absence of a phrase must be interpreted as the absence of any inferrable phrase--adding a phrase silently will increase acceptability, but this should be avoided in order to understand the judgments. It is also intended that a difference in transitivity not change the meaning of the verb, so sometimes a * might indicate that example is not interpretable in the same way as the corresponding non-*ed examples.)
*Al slept a man.
Al watched TV.
*Al gave a ring.
*Al watched Mary TV.
*Al watched TV to Mary.
Al gave Mary a ring.
Al gave a ring to Mary.
Single-event compatibility with "in"-phrases:
*Al slept in an hour.
*Al watched TV in an hour.
Al gave Mary a ring in a year.
Single event compatibility with "for"-adverbials:
Al slept for an hour.
Al watched TV for an hour.
*Al gave Mary a ring for a year.
Entailment from the progressive to the perfect:
Al is sleeping. => Al has slept.
Al is watching TV. => Al has watched TV.
Al is giving Mary a ring. !=> Al has given Mary a ring.
Single-event compatibility with "a lot":
Al slept a lot last night.
Al watched TV a lot last night.
*Al gave Mary a ring a lot last night.